2016 
Borwein JM, Giladi O, 'NEAREST POINTS AND DELTA CONVEX FUNCTIONS IN BANACH SPACES', Bulletin of the Australian Mathematical Society, 93 283294 (2016)
Â© 2015 Australian Mathematical Publishing Association Inc.Given a closed set C in a Banach space (X,  Â· ), a point x Â¿ X is said to have a nearest point in C if there exist... [more]
Â© 2015 Australian Mathematical Publishing Association Inc.Given a closed set C in a Banach space (X,  Â· ), a point x Â¿ X is said to have a nearest point in C if there exists z Â¿ C such that dC(x) = x  z, where dC is the distance of x from C. We survey the problem of studying the size of the set of points in X which have nearest points in C. We then turn to the topic of delta convex functions and indicate how it is related to finding nearest points.



2016 
Borwein JM, Giladi O, 'Convex analysis in groups and semigroups: a sampler', Mathematical Programming, 143 (2016)



2016 
AragÃ³n Artacho FJ, Borwein JM, Tam MK, 'Global behavior of the DouglasÂ¿Rachford method for a nonconvex feasibility problem', Journal of Global Optimization, 65 309327 (2016)
Â© 2015, Springer Science+Business Media New York.In recent times the DouglasÂ¿Rachford algorithm has been observed empirically to solve a variety of nonconvex feasibility problem... [more]
Â© 2015, Springer Science+Business Media New York.In recent times the DouglasÂ¿Rachford algorithm has been observed empirically to solve a variety of nonconvex feasibility problems including those of a combinatorial nature. For many of these problems current theory is not sufficient to explain this observed success and is mainly concerned with questions of local convergence. In this paper we analyze global behavior of the method for finding a point in the intersection of a halfspace and a potentially nonconvex set which is assumed to satisfy a wellquasiordering property or a property weaker than compactness. In particular, the special case in which the second set is finite is covered by our framework and provides a prototypical setting for combinatorial optimization problems.



2016 
Borwein JM, Straub A, Vignat C, 'Densities of short uniform random walks in higher dimensions', Journal of Mathematical Analysis and Applications, 437 668707 (2016)
Â© 2016 Elsevier Inc.We study arithmetic properties of short uniform random walks in arbitrary dimensions, with a focus on explicit (hypergeometric) evaluations of the moment func... [more]
Â© 2016 Elsevier Inc.We study arithmetic properties of short uniform random walks in arbitrary dimensions, with a focus on explicit (hypergeometric) evaluations of the moment functions and probability densities in the case of up to five steps. Somewhat to our surprise, we are able to provide complete extensions to arbitrary dimensions for most of the central results known in the twodimensional case.



2016 
Borwein JM, Sinnamon CW, 'A CLOSED FORM FOR THE DENSITY FUNCTIONS OF RANDOM WALKS IN ODD DIMENSIONS', Bulletin of the Australian Mathematical Society, 93 330339 (2016)



2015 
Borwein JM, Bugeaud Y, Coons M, 'The Legacy of Kurt Mahler', Notices of the American Mathematical Society, 62 526531 (2015) [C3]



2015 
Bailey DH, Borwein JM, 'COMPUTATION AND STRUCTURE OF CHARACTER POLYLOGARITHMS WITH APPLICATIONS TO CHARACTER MORDELLTORNHEIMWITTEN SUMS', MATHEMATICS OF COMPUTATION, 85 295324 (2015)



2015 
Bailey DH, Borwein JM, 'Crandall's computation of the incomplete Gamma function and the Hurwitz zeta function, with applications to Dirichlet Lseries', APPLIED MATHEMATICS AND COMPUTATION, 268 462477 (2015) [C1]



2015 
Borwein JM, Straub A, 'Relations for Nielsen polylogarithms', Journal of Approximation Theory, 193 7488 (2015) [C1]



2015 
Bailey DH, Borwein D, Borwein JM, 'On Eulerian loggamma integrals and TornheimÂ¿Witten zeta functions', Ramanujan Journal, 36 4368 (2015) [C1]
Â© 2012, Springer Science+Business Media.Stimulated by earlier work by Moll and his coworkers (Amdeberhan et al., Proc. Am. Math. Soc., 139(2):535Â¿545, 2010), we evaluate various... [more]
Â© 2012, Springer Science+Business Media.Stimulated by earlier work by Moll and his coworkers (Amdeberhan et al., Proc. Am. Math. Soc., 139(2):535Â¿545, 2010), we evaluate various basic log Gamma integrals in terms of partial derivatives of TornheimÂ¿Witten zeta functions and their extensions arising from evaluations of Fourier series. In particular, we fully evaluate Formula presented for 1 = n = 4 and make some comments regarding the general case. The subsidiary computational challenges are substantial, interesting and significant in their own right.



2015 
Borwein JM, Zhu QJ, 'A Variational Approach to Lagrange Multipliers', Journal of Optimization Theory and Applications, (2015)



2015 
Borwein JM, Tam MK, 'The cyclic DouglasRachford method for inconsistent feasibility problems', Journal of Nonlinear and Convex Analysis, 16 537584 (2015) [C1]



2015 
Borwein JM, Sims B, Tam MK, 'Norm convergence of realistic projection and reflection methods', Optimization, 64 161178 (2015) [C1]



2015 
Borwein JM, Chapman ST, 'I Prefer Pi: A Brief History and Anthology of Articles in the American Mathematical Monthly', AMERICAN MATHEMATICAL MONTHLY, 122 195216 (2015) [C1]



2015 
Bailey DH, Borwein JM, 'Computation and theory of MordellTornheimWitten sums II', Journal of Approximation Theory, 197 115140 (2015) [C1]
Â© 2014 Elsevier Inc.In Bailey etal. [8] the current authors, along with the late and muchmissed Richard Crandall (19472012), considered generalized MordellTornheimWitten (MTW... [more]
Â© 2014 Elsevier Inc.In Bailey etal. [8] the current authors, along with the late and muchmissed Richard Crandall (19472012), considered generalized MordellTornheimWitten (MTW) zetafunction values along with their derivatives, and explored connections with multiplezeta values (MZVs). This entailed use of symbolic integration, high precision numerical integration, and some interesting combinatorics and specialfunction theory. The original motivation was to represent objects such as Eulerian loggamma integrals; and all such integrals were expressed in terms of a MTW basis. Herein, we extend the research envisaged in Bailey etal. [8] by analyzing the relations between a significantly more general class of MTW sums. This has required significantly more subtle scientific computation and concomitant special function theory.



2015 
Borwein JM, Dutta J, 'Maximal Monotone Inclusions and Fitzpatrick Functions', Journal of Optimization Theory and Applications, (2015)
Â© 2015 Springer Science+Business Media New YorkIn this paper, we study maximal monotone inclusions from the perspective of gap functions. We propose a very natural gap function f... [more]
Â© 2015 Springer Science+Business Media New YorkIn this paper, we study maximal monotone inclusions from the perspective of gap functions. We propose a very natural gap function for an arbitrary maximal monotone inclusion and will demonstrate how naturally this gap function arises from the Fitzpatrick function, which is a convex function, used to represent maximal monotone operators. This allows us to use the powerful strong Fitzpatrick inequality to analyse solutions of the inclusion. We also study the special cases of a variational inequality and of a generalized variational inequality problem. The associated notion of a scalar gap is also considered in some detail. Corresponding local and global error bounds are also developed for the maximal monotone inclusion.



2014 
Artacho FJA, Borwein JM, Tam MK, 'Recent Results on DouglasRachford Methods for Combinatorial Optimization Problems', JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 163 130 (2014) [C1]



2014 
Borwein D, Borwein J, 'Deriving New Sine Results from Old', AMERICAN MATHEMATICAL MONTHLY, 121 700705 (2014)



2014 
Borwein D, Borwein JM, Sims B, 'On the Solution of Linear Mean Recurrences', AMERICAN MATHEMATICAL MONTHLY, 121 486498 (2014) [C1]



2014 
Bailey DH, Borwein J, 'Pi day is upon us again and we still do not know if Pi is normal', American Mathematical Monthly, 121 191206 (2014) [C1]



2014 
Bailey DH, Borwein JM, de Prado ML, Zhu QJ, 'Pseudomathematics and financial charlatanism: The effects of backtest overfitting on outofsample performance', Notices of the American Mathematical Society, 61 458471 (2014) [C1]



2014 
Borwein D, Borwein JM, Straub A, 'On lattice sums and Wigner limits', Journal of Mathematical Analysis and Applications, 414 489513 (2014) [C1]
Wigner limits are given formally as the difference between a lattice sum, associated to a positive definite quadratic form, and a corresponding multiple integral. To define these ... [more]
Wigner limits are given formally as the difference between a lattice sum, associated to a positive definite quadratic form, and a corresponding multiple integral. To define these limits, which arose in work of Wigner on the energy of static electron lattices, in a mathematically rigorous way one commonly truncates the lattice sum and the corresponding integral and takes the limit along expanding hypercubes or other regular geometric shapes. We generalize the known mathematically rigorous two and threedimensional results regarding Wigner limits, as laid down in [3], to integer lattices of arbitrary dimension. In doing so, we also resolve a problem posed in [6, Chapter 7]. For the sake of clarity, we begin by considering the simpler case of cubic lattice sums first, before treating the case of arbitrary quadratic forms. We also consider limits taken along expanding hyperballs with respect to general norms, and connect with classical topics such as Gauss's circle problem. Appendix A is included to recall certain properties of Epstein zeta functions that are either used in the paper or serve to provide perspective. Â© 2014 Elsevier Inc.



2014 
Borwein JM, Tam MK, 'A Cyclic DouglasRachford Iteration Scheme', JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 160 129 (2014) [C1]



2014 
AragÃ³n Artacho FJ, Borwein JM, MartÃnMÃ¡rquez V, Yao L, 'Applications of convex analysis within mathematics', Mathematical Programming, 148 4988 (2014) [C1]



2014 
Bailey DH, Borwein JM, Crandall RE, 'COMPUTATION AND THEORY OF EXTENDED MORDELLTORNHEIMWITTEN SUMS', MATHEMATICS OF COMPUTATION, 83 17951821 (2014) [C1]



2014 
James D, WilkinsDiehr N, Stodden V, Colbry D, Rosales C, Fahey MR, et al., 'Standing Together for Reproducibility in LargeScale Computing: Report on reproducibility@XSEDE.', CoRR, abs/1412.5557 (2014) 


2014 
Bailey DH, Borwein JM, Kaiser AD, 'Automated simplification of large symbolic expressions', JOURNAL OF SYMBOLIC COMPUTATION, 60 120136 (2014) [C1]



2014 
Borwein JM, Yao L, 'LegendreType Integrands and Convex Integral Functions', JOURNAL OF CONVEX ANALYSIS, 21 261288 (2014) [C1] 


2014 
Borwein JM, Li G, Yao L, 'ANALYSIS OF THE CONVERGENCE RATE FOR THE CYCLIC PROJECTION ALGORITHM APPLIED TO BASIC SEMIALGEBRAIC CONVEX SETS', SIAM JOURNAL ON OPTIMIZATION, 24 498527 (2014) [C1]



2014 
Borwein J, Howlett P, Piantadosi J, 'Modelling and Simulation of Seasonal Rainfall Using the Principle of Maximum Entropy', ENTROPY, 16 747769 (2014) [C1]



2014 
Borwein JM, Burachik RS, Yao L, 'Conditions for zero duality gap in convex programming', Journal of Nonlinear and Convex Analysis, 15 167190 (2014) [C1]
We introduce and study a new dual condition which characterizes zero duality gap in nonsmooth convex optimization. We prove that our condition is less restrictive than all existin... [more]
We introduce and study a new dual condition which characterizes zero duality gap in nonsmooth convex optimization. We prove that our condition is less restrictive than all existing constraint qualifications, including the closed epigraph condition. Our dual condition was inspired by, and is less restrictive than, the socalled Bertsekas' condition for monotropic programming problems. We give several corollaries of our result and special cases as applications. We pay special attention to the polyhedral and sublinear cases, and their implications in convex optimization. Â©2014.



2014 
Artacho FJA, Borwein JM, Tam MK, 'Douglasrachford feasibility methods for matrix completion problems', ANZIAM Journal, 55 299326 (2014) [C1]



2014 
BORWEIN JM, YAO L, 'SUM THEOREMS FOR MAXIMALLY MONOTONE OPERATORS OF TYPE (FPV)', Journal of the Australian Mathematical Society, (2014) [C1]



2014 
Borwein JM, Yao L, 'Some results on the convexity of the closure of the domain of a maximally monotone operator', OPTIMIZATION LETTERS, 8 237246 (2014) [C1]



2013 
Borwein JM, Crandall RE, 'Closed Forms: What they are and why we care', Notices of the American Mathematical Society, 60 5065 (2013) [C1]



2013 
Bailey DH, Borwein JM, Mattingly A, Wightwick G, 'The computation of previously inaccessible digits of p2 and Catalan's constant', Notices of the American Mathematical Society, 60 844854 (2013) [C1]



2013 
Borwein JM, Yao L, 'Structure Theory for Maximally Monotone Operators with Points of Continuity', Journal of Optimization Theory and Applications, 157 124 (2013) [C1]



2013 
AragÃ³n Artacho FJ, Borwein JM, MartÃnMÃ¡rquez V, Yao L, 'Applications of convex analysis within mathematics', Mathematical Programming, 148 4988 (2013)
Â© 2013, SpringerVerlag Berlin Heidelberg and Mathematical Optimization Society.In this paper, we study convex analysis and its theoretical applications. We first apply important... [more]
Â© 2013, SpringerVerlag Berlin Heidelberg and Mathematical Optimization Society.In this paper, we study convex analysis and its theoretical applications. We first apply important tools of convex analysis to Optimization and to Analysis. We then show various deep applications of convex analysis and especially infimal convolution in Monotone OperatorÂ¿ Theory. Among other things, we recapture the Minty surjectivity theorem in Hilbert space, and present a new proof of the sum theorem in reflexive spaces. More technically, we also discuss autoconjugate representers for maximally monotone operators. Finally, we consider various other applications in mathematical analysis.



2013 
Bailey DH, Borwein JM, Crandall RE, Rose MG, 'Expectations on fractal sets', APPLIED MATHEMATICS AND COMPUTATION, 220 695721 (2013) [C1]



2013 
Borwein JM, Straub A, 'Mahler measures, short walks and logsine integrals', THEORETICAL COMPUTER SCIENCE, 479 421 (2013) [C1]



2013 
Artacho FJA, Bailey DH, Borwein JM, Borwein PB, 'Walking on Real Numbers', MATHEMATICAL INTELLIGENCER, 35 4260 (2013) [C1]



2013 
Artacho FJA, Borwein JM, 'Global convergence of a nonconvex DouglasRachford iteration', JOURNAL OF GLOBAL OPTIMIZATION, 57 753769 (2013) [C1]



2013 
Bauschke HH, Borwein JM, Wang X, Yao L, 'Monotone Operators and "Bigger Conjugate" Functions', JOURNAL OF CONVEX ANALYSIS, 20 143155 (2013) [C1]



2013 
Borwein JM, Straub A, Wan J, 'ThreeStep and FourStep Random Walk Integrals', Experimental Mathematics, 22 114 (2013) [C1]



2013 
AragÃ³n Artacho FJ, Borwein JM, Tam MK, 'Recent Results on DouglasRachford Methods', Serdica Mathematical Journal, 39 313330 (2013) [C1] 


2013 
Bailey DH, Borwein JM, 'Compressed lattice sums arising from the Poisson equation', BOUNDARY VALUE PROBLEMS, (2013) [C1]



2013 
Bailey DH, Borwein JM, Crandall RE, Zucker IJ, 'Lattice sums arising from the Poisson equation', Journal of Physics A: Mathematical and Theoretical, 46 (2013) [C1]



2013 
Borwein JM, Crandall RE, 'Closed Forms: What they are and why we care', Notices of the American Mathematical Society, 60 5065 (2013)



2013 
Borwein JM, Yao L, 'Maximality of the Sum of a Maximally Monotone Linear Relation and a Maximally Monotone Operator', SETVALUED AND VARIATIONAL ANALYSIS, 21 603616 (2013) [C1]



2013 
Borwein JM, Zhu QJ, 'Variational methods in the presence of symmetry', Advances in Nonlinear Analysis, 2 (2013) [C1]



2012 
Borwein D, Borwein JM, Straub A, 'A sinc that sank', American Mathematical Monthly, 119 535549 (2012) [C1]



2012 
Bailey DH, Borwein JM, 'Ancient Indian square roots: An exercise in forensic paleomathematics', American Mathematical Monthly, 119 646657 (2012) [C1]



2012 
Borwein JM, 'Ramanujan and Pi', American Mathematical Society. Notices, 59 15341537 (2012) [C1] 


2012 
Borwein JM, Jungic V, 'Organic mathematics then and now', Notices of the AMS, 59 416419 (2012) [C2] 


2012 
Borwein JM, Straub A, Wan G, Zudilin V, 'Densities of short uniform random walks', Canadian Journal of Mathematics, 64 961990 (2012) [C1]



2012 
Borwein JM, Vanderwerff J, 'Constructions of uniformly convex functions', Canadian Mathematical Bulletin, 55 697707 (2012) [C1] 


2012 
Bauschke HH, Borwein JM, Wang X, Yao L, 'The BrezisBrowder Theorem in a general Banach space', Journal of Functional Analysis, 262 49484971 (2012) [C1]



2012 
Amdeberhan T, Borwein D, Borwein JM, Straub A, 'On formulas for Pi experimentally conjectured by JaureguiTsallis', Journal of Mathematical Physics, 53 (2012) [C1] 


2012 
Bailey DH, Barrio R, Borwein JM, 'Highprecision computation: Mathematical physics and dynamics', Applied Mathematics and Computation, 218 1010610121 (2012) [C1]



2012 
Borwein JM, 'Maximum entropy and feasibility methods for convex and nonconvex inverse problems', Optimization, 61 133 (2012) [C1]



2012 
Bailey DH, Borwein JM, Calude CS, Dinneen MJ, Dumitrescu M, Yee A, 'An empirical approach to the normality of p', Experimental Mathematics, 21 375384 (2012) [C1]



2012 
Borwein JM, Borwein P, Jungic V, 'Remote collaboration: Six years of the CoasttoCoast Seminar Series', Science Communication, 34 419428 (2012) [C3] 


2012 
Bailey DH, Borwein JM, 'Nonnormality of Stoneham constants', Ramanujan Journal, 29 409422 (2012) [C1]



2012 
Alladi K, Andrews GE, Borwein JM, 'Preface. Ramanujan's 125th Anniversary Special Volume', Ramanujan Journal, 29 12 (2012) [C3]



2012 
Borwein JM, Osborn JAH, 'Response to 'Experimental Approaches to Theoretical Thinking: Artefacts and Proofs Proof and Proving in Mathematics Education'', Proof and Proving in Mathematics Education: The 19th ICMI Study, 15 138143 (2012) [C3]



2012 
Borwein JM, Straub A, 'Logsine evaluations of Mahler measures', Journal of the Australian Mathematical Society, 92 1536 (2012) [C1]



2012 
Piantadosi J, Howlett P, Borwein JM, 'Copulas with maximum entropy', Optimization Letters, 6 99125 (2012) [C1]



2012 
Bauschke HH, Borwein JM, Wang X, Yao L, 'Every maximally monotone operator of FitzpatrickPhelps type is actually of dense type', Optimization Letters, 6 18751881 (2012) [C1]



2012 
Borwein JM, Osborn JAH, 'Loving and Hating Mathematics by Reuben Hersh and Vera JohnSteiner [Book Review]', The Mathematical Intelligencer, 33 6369 (2012) [C3] 


2012 
Borwein D, Borwein JM, Straub A, Wan G, 'Logsine evaluations of Mahler measures, II', Integers, 12 11791212 (2012) [C1] 


2012 
Wang XF, Yao L, Bauschke HH, Borwein JM, 'Construction of pathological maximally monotone operators on nonreflexive Banach spaces', SetValued and Variational Analysis, 20 387415 (2012) [C1]



2012 
Bailey DH, Borwein JM, 'Handtohand combat with thousanddigit integrals', Journal of Computational Science, 3 7786 (2012) [C1]



2012 
Janssen H, Craxi A, 'Preface', BEST PRACTICE & RESEARCH IN CLINICAL GASTROENTEROLOGY, 26 369369 (2012)



2012 
Piantadosi J, Howlett P, Borwein J, Henstridge J, 'Maximum entropy methods for generating simulated rainfall', Numerical Algebra, Control and Optimization, 2 233256 (2012) [C1]
We desire to generate monthly rainfall totals for a particular loca tion in such a way that the statistics for the simulated data match the statistics for the observed data. We a... [more]
We desire to generate monthly rainfall totals for a particular loca tion in such a way that the statistics for the simulated data match the statistics for the observed data. We are especially interested in the accumulated rainfall totals over several months. We propose two different ways to construct a joint rainfall probability distribution that matches the observed grade correlation coefficients and preserves the prescribed marginal distributions. Both methods use multidimensional checkerboard copulas. In the first case we use the the ory of Fenchel duality to construct a copula of maximum entropy and in the second case we use a copula derived from a multivariate normal distribution. Finally we simulate monthly rainfall totals at a particular location using each method and analyse the statistical behaviour of the corresponding quarterly accumulations.



2011 
Borwein JM, Straub A, 'Special Values of Generalized Logsine Integrals', CoRR, abs/1103.4298 (2011) 


2011 
Bailey DH, Borwein JM, 'Exploratory experimentation and computation', Notices of the American Mathematical Society, 58 14101419 (2011) [C1]



2011 
Borwein D, Borwein JM, Glasser ML, Wan G, 'Moments of Ramanujan's generalized elliptic integrals and extensions of Catalan's constant', Journal of Mathematical Analysis and Applications, 384 478496 (2011) [C1]



2011 
Bacak M, Borwein JM, 'On difference convexity of locally Lipschitz functions', Optimization, 60 961978 (2011) [C1]



2011 
Borwein JM, Osborn JA, 'Review: Hersh, R. and JohnSteiner, V. Loving and Hating Mathematics', Mathematical Intelligencer, 33 6369 (2011) [C3]



2011 
Bailey DH, Borwein JM, 'Highprecision numerical integration: Progress and challenges', Journal of Symbolic Computation, 46 741754 (2011) [C1]



2011 
Borwein JM, 'Review: Dontchev, A.L. and Rockafellar, R.T, Implicit Functions and Solution Mappings', IEEE Control Systems, 31 7477 (2011) [C3] 


2011 
Borwein JM, Reich S, Sabach S, 'A characterization of Bregman firmly nonexpansive operators using a new monotonicity concept', Journal of Nonlinear and Convex Analysis, 12 161184 (2011) [C1]



2011 
Borwein JM, Nuyens D, Straub A, Wan G, 'Some arithmetic properties of short random walk integrals', Ramanujan Journal, 26 109132 (2011) [C1]



2010 
Borwein JM, Chan OY, 'Duality in tails of multiplezeta values', International Journal of Number Theory, 6 501514 (2010) [C1]



2010 
Borwein JM, 'Fifty years of maximal monotonicity', Optimization Letters, 4 473490 (2010) [C1]



2010 
Borwein JM, Morrs WB, 'Stability of closedness of convex cones under linear mappings II', Journal of Nonlinear Analysis and Optimization: Theory and Applications, 1 17 (2010) [C1] 


2010 
Borwein D, Borwein JM, Leonard IE, 'Lp norms and the sine function', American Mathematical Monthly, 117 528539 (2010) [C1]



2010 
Bailey DH, Borwein JM, Crandall RE, 'Advances in the theory of box integrals', Mathematics of Computation, 79 18391866 (2010) [C1]



2010 
Bailey DH, Borwein JM, Broadhurst D, Zudilin V, 'Experimental mathematics and mathematical physics', Contemporary Mathematics, 517 4158 (2010) [C1]



2010 
Bailey DH, Borwein JM, 'Experimental computation with oscillatory integrals', Contemporary Mathematics, 517 2540 (2010) [C1]



2010 
Bacak M, Borwein JM, Eberhard A, Mordukhovich BS, 'Infimal convolutions and lipschitzian properties of subdifferentials for proxregular functions in hilbert spaces', Journal of Convex Analysis, 17 737763 (2010) [C1]



2010 
Borwein JM, Vanderwerff J, 'Frechetlegendre functions and reflexive banach spaces', Journal of Convex Analysis, 17 915924 (2010) [C1]



2010 
Borwein JM, Chan OY, Crandall RE, 'Higherdimensional box integrals', Experimental Mathematics, 19 431446 (2010) [C1]



2009 
Bailey DH, Borwein JM, 'Experimental mathematics and computational statistics', WIREs Computational Statistics, 1 1224 (2009) [C1]



2009 
Borwein JM, Calkin NJ, Manna D, 'EulerBoole Summation Revisited', AMERICAN MATHEMATICAL MONTHLY, 116 387412 (2009) [C1]



2009 
Borwein JM, Guirao AJ, Hajek P, Vanderwerff J, 'Uniformly convex functions on Banach Spaces', Proceedings of the American Mathematical Society, 137 10811091 (2009) [C1]



2009 
Borwein JM, 'The Princeton companion to mathematics', SIAM Review, 51 790794 (2009) [C3] 


2009 
Borwein JM, Vanderwerff J, 'Differentiability of conjugate functions and perturbed minimization principles', Journal of Convex Analysis, 16 707711 (2009) [C1]



2009 
Borwein JM, Moors WB, 'Stability of closedness of convex cones under linear mappings', Journal of Convex Analysis, 16 699705 (2009) [C1]



2009 
Bailey DH, Borwein JM, Crandall RE, 'Resolution of the QuinnRandStrogatz Constant of nonlinear physics', Experimental Mathematics, 18 107116 (2009) [C1]



2009 
Borwein JM, Chan OY, 'UNIFORM BOUNDS FOR THE COMPLEMENTARY INCOMPLETE GAMMA FUNCTION', MATHEMATICAL INEQUALITIES & APPLICATIONS, 12 115121 (2009) [C1]



2008 
Borwein JM, Salvy B, 'A Proof of a Recurrence for Bessel Moments.', Experimental Mathematics, 17 223230 (2008) [C1]



2008 
Borwein JM, Salvy B, 'A Proof of a Recurrence for Bessel Moments', Experimental Mathematics, 17 223230 (2008) [C1]



2008 
Borwein JM, Luke DR, 'Dynamics of a Ramanujantype Continued Fraction with Cyclic Coefficients', The Ramanujan Journal: an international journal devoted to areas of mathematics influenced by Ramanu, 16 285304 (2008) [C1]



2008 
Borwein JM, Zucker IJ, Boersma J, 'The evaluation of character Euler double sums', The Ramanujan Journal: an international journal devoted to areas of mathematics influenced by Ramanu, 15 377405 (2008) [C1]



2008 
Bailey DH, Borwein JM, Broadhurst DM, Glasser L, 'Elliptic integral evaluations of Bessel moments and applications', Journal of Physics A: Mathematical and Theoretical, 41 52035231 (2008) [C1]



2008 
Baillie R, Borwein D, Borwein JM, 'Surprising sinc sums and integrals', American Mathematical Monthly, 115 888901 (2008) [C1]



2008 
Borwein JM, 'Hilbert's Inequality and Witten's ZetaFunction', American Mathematical Monthly, 115 125137 (2008) [C1]



2008 
Borwein D, Borwein JM, Chan OY, 'The Evaluation of Bessel Functions via ExpArc Integrals', Journal of Mathematical Analysis and Applications, 341 478500 (2008) [C1]



2008 
Borwein D, Borwein JM, Crandall RE, 'Effective Laguerre Asymptotics', SIAM Journal on Numerical Analysis, 46 32853312 (2008) [C1]



2008 
Eberhard AC, Borwein JM, 'Second Order Cones for Maximal Monotone Operators via Representative Functions', SetValued and Variational Analysis: an international journal devoted to the theory of multifunctions, 16 157184 (2008) [C1]



2007 
Bartz S, Bauschke HH, Borwein JM, Reich S, Wang X, 'Fitzpatrick functions, cyclic monotonicity and Rockafellar's antiderivative', NONLINEAR ANALYSISTHEORY METHODS & APPLICATIONS, 66 11981223 (2007) [C1]



2007 
Bailey DH, Borwein JM, Crandall RE, 'Box integrals', JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 206 196208 (2007) [C1]



2007 
Bauschke HH, Borwein JM, Wang X, 'Fitzpatrick functions and continuous linear monotone operators', SIAM JOURNAL ON OPTIMIZATION, 18 789809 (2007) [C1]



2007 
Borwein J, Wiersma H, 'Asplund decomposition of monotone operators', SIAM JOURNAL ON OPTIMIZATION, 18 946960 (2007) [C1]



2007 
Bailey DH, Borwein D, Borwein JM, Crandall RE, 'Hypergeometric forms for isingclass integrals', EXPERIMENTAL MATHEMATICS, 16 257276 (2007) [C1]



2007 
Borwein D, Borwein J, Crandall R, Mayer R, 'On the dynamics of certain recurrence relations', RAMANUJAN JOURNAL, 13 63101 (2007) [C1]



2007 
Borwein JM, 'Proximality and Chebyshev sets', OPTIMIZATION LETTERS, 1 2132 (2007) [C1]



2007 
Borwein JM, Moors WB, 'Nonsmooth Analysis, Optimisation Theory and Banach Space Theory 549559 (2007)
This chapter discusses about nonsmooth analysis, optimization theory, and Banach space theory. A Banach space X is called a weak Asplund space [GÃ¢teaux differentiability space] i... [more]
This chapter discusses about nonsmooth analysis, optimization theory, and Banach space theory. A Banach space X is called a weak Asplund space [GÃ¢teaux differentiability space] if each continuous convex function defined on it is GÃ¢teaux differentiable at the points of a residual subset (that is, a subset that contains the intersection of countably many dense open subsets of X) [dense subset] of its domain. For a Banach space (X, Â¿ Â·. Â¿), with closed unit ball BX, the BishopPhelps set is the set of all linear functionals in the dual X* that attain their maximum value over BX; that is, the set {. x*Â¿. X*: x*(x) = Â¿. x*Â¿ for some x Â¿. BX}. The BishopPhelps Theorem says that the BishopPhelps set is always dense in X*. A Banach space X has the attainable approximation property (AAP) if the set of support functionals for any closed bounded convex subset W Â¿. X is norm dense in X*. The concepts related to the BishopPhelps problem and the complex BishopPhelps property are also discussed. Concepts of biorthogonal sequences and support points are also elaborated. Â© 2007 Elsevier B.V. All rights reserved.



2007 
Borwein JM, Langstroth D, Macklem M, Wilson S, Jungic V, 'The coasttocoast seminar and remote mathematical collaboration', Proceedings  International Symposium on High Performance Computing Systems and Applications, (2007)



2007 
Borwein JM, 'A class of Dirichlet series integrals', AMERICAN MATHEMATICAL MONTHLY, 114 7076 (2007) [C1]



2007 
Bailey D, Borwein J, Bradley D, 'A hypergeometric identity', AMERICAN MATHEMATICAL MONTHLY, 114 643645 (2007) 


2007 
Borwein JM, 'Maximality of sums of two maximal monotone operators in general banach space', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 135 39173924 (2007) [C1]



2007 
Borwein D, Borwein J, 'van der pol expansions of Lseries', CANADIAN MATHEMATICAL BULLETINBULLETIN CANADIEN DE MATHEMATIQUES, 50 1123 (2007) [C1]



2007 
Borwein JM, Chamberland M, 'Integer powers of Arcsin', International Journal of Mathematics and Mathematical Sciences, 2007 110 (2007) [C1]



2006 
Borwein D, Borwein JM, Bradley DM, 'Parametric Euler sum identities', JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 316 328338 (2006) [C1]



2006 
Bailey DH, Borwein JM, Crandall RE, 'Integrals of the Ising class', JOURNAL OF PHYSICS AMATHEMATICAL AND GENERAL, 39 1227112302 (2006) [C1]



2006 
Borwein JM, Zhu QJJ, 'Variational methods in convex analysis', JOURNAL OF GLOBAL OPTIMIZATION, 35 197213 (2006) [C1]



2006 
Borwein J, 'Simon Fitzpatrick memorial volume', JOURNAL OF CONVEX ANALYSIS, 13 463476 (2006)



2006 
Borwein JM, 'Maximal monotonicity via convex analysis', JOURNAL OF CONVEX ANALYSIS, 13 561586 (2006) [C1]



2006 
Borwein J, Montesinos V, Vanderwerff J, 'Boundedness, differentiability and extensions of convex functions', JOURNAL OF CONVEX ANALYSIS, 13 587602 (2006) [C1]



2006 
Borwein JM, 'The Life of Simon Fitzpatrick, 19532004', Journal of Convex Analysis, 13 463476 (2006) [C1] 


2006 
Borwein JM, Bradley DM, 'Thirtytwo goldbach variations', INTERNATIONAL JOURNAL OF NUMBER THEORY, 2 65103 (2006) [C1]



2006 
Bailey DH, Borwein JM, 'Effective bounds in EulerMaclaurinbased quadrature (summary for HPCS06)', 20th International Symposium on HighPerformance Computing in an Advanced Collaborative Environment, 2006. HPCS 2006, 34 (2006)
We analyze the behavior of EulerMaclaurinbased integration schemes with the intention of deriving accurate and economic estimations of the error. These schemes typically provide... [more]
We analyze the behavior of EulerMaclaurinbased integration schemes with the intention of deriving accurate and economic estimations of the error. These schemes typically provide very highprecision results (hundreds or thousands of digits), in reasonable run time, even in cases where the integrand function has a blowup singularity or infinite derivative at an endpoint. Heretofore, researchers using these schemes have relied mostly on ad hoc error estimation schemes to project the estimated error of the present iteration. In this paper, we seek to develop some more rigorous, yet highly usable schemes to estimate these errors. Â© 2006 IEEE.



2006 
Bailey DH, Borwein JM, Bradley DM, 'Experimental determination of Aperylike identities for zeta(2n+2)', EXPERIMENTAL MATHEMATICS, 15 281289 (2006) [C1]



2006 
Bailey DH, Borwein JM, Kapoor V, Weisstein EW, 'Ten problems in experimental mathematics', AMERICAN MATHEMATICAL MONTHLY, 113 481509 (2006) [C1]



2006 
Borwein JM, 'Maximality of sums of two maximal monotone operators', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 134 29512955 (2006) [C1]



2005 
Borwein JM, Girgensohn R, 'Evaluations of binomial series', Aequationes Mathematicae, 70 2536 (2005) [C1]



2005 
Borwein JM, Choi KKS, Pigulla W, 'Continued fractions of tails of hypergeometric series', AMERICAN MATHEMATICAL MONTHLY, 112 493501 (2005) [C1]



2005 
Bailey DH, Borwein JM, 'Experimental mathematics: Examples, methods and implications', Notices of the American Mathematical Society, 52 502514 (2005) [C1]



2005 
Borwein JM, Wang XF, 'Lipschitz functions with maximal Clarke subdifferentials are staunch', BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 72 491496 (2005) [C1]



2005 
Borwein JM, Wang XF, 'Conemonotone functions: Differentiability and continuity', CANADIAN JOURNAL OF MATHEMATICSJOURNAL CANADIEN DE MATHEMATIQUES, 57 961982 (2005) [C1]



2005 
Borwein J, Stanway T, 'Knowledge and community in mathematics', MATHEMATICAL INTELLIGENCER, 27 716 (2005) [C1]



2005 
Borwein JM, 'The SIAM 100 Digits Challenge', The Mathematical Intelligencer, 27 4048 (2005) [C3] 


2005 
Borwein JM, Luke DR, 'Dynamics of a continued fraction of Ramanujan with random coefficients', ABSTRACT AND APPLIED ANALYSIS, 449467 (2005) [C1]



2005 
Borwein JM, 'The experimental mathematician: The pleasure of discovery and the role of proof', International Journal of Computers for Mathematical Learning, 10 75108 (2005) [C1]
The emergence of powerful mathematical computing environments, the growing availability of correspondingly powerful (multiprocessor) computers and the pervasive presence of the i... [more]
The emergence of powerful mathematical computing environments, the growing availability of correspondingly powerful (multiprocessor) computers and the pervasive presence of the internet allow for mathematicians, students and teachers, to proceed heuristically and 'quasiinductively'. We may increasingly use symbolic and numeric computation, visualization tools, simulation and data mining. The unique features of our discipline make this both more problematic and more challenging. For example, there is still no truly satisfactory way of displaying mathematical notation on the web; and we care more about the reliability of our literature than does any other science. The traditional role of proof in mathematics is arguably under siege  for reasons both good and bad. Â© Springer 2005.



2004 
Borwein JM, Burke JV, Lewis AS, 'Differentiability of conemonotone functions on separable Banach space', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 132 10671076 (2004) [C1]



2004 
Borwein JM, Borwein D, Galway WF, 'Finding and excluding bary Machintype individual digit formulae', CANADIAN JOURNAL OF MATHEMATICSJOURNAL CANADIEN DE MATHEMATIQUES, 56 897925 (2004) [C1]



2004 
Borwein J, Cheng LX, Fabian M, Revalski JP, 'A one perturbation variational principle and applications', SETVALUED ANALYSIS, 12 4960 (2004) [C1]



2004 
Borwein JM, Vanderwerff JD, 'Constructible convex sets', SETVALUED ANALYSIS, 12 6177 (2004) [C1]



2004 
Borwein J, Crandall R, Fee G, 'On the Ramanujan AGM fraction, I: The realparameter case', EXPERIMENTAL MATHEMATICS, 13 275285 (2004) [C1]



2004 
Borwein J, Crandall R, 'On the Ramanujan AGM fraction, II: The complex parameter case', EXPERIMENTAL MATHEMATICS, 13 287295 (2004) [C1]



2004 
Bailey D, Borwein JM, Crandall R, Pomerance C, 'On the binary expansions of algebraic numbers', Journal de Theorie des Nombres de Bordeaux, 16 487518 (2004) [C1] 


2003 
Borwein J, Girgensohn R, 'A class of exponential inequalities', MATHEMATICAL INEQUALITIES & APPLICATIONS, 6 397411 (2003) [C1]



2003 
Borwein JM, Choi KKS, 'On Dirichlet series for sums of squares', RAMANUJAN JOURNAL, 7 95127 (2003) [C1]



2003 
Kellar M, MacKay B, Zhang R, Watters C, Kaufman D, Borwein J, 'Dynamic composition of math lessons', EDUCATIONAL TECHNOLOGY & SOCIETY, 6 100111 (2003) [C1]



2003 
Borwein D, Borwein JM, Rooin J, 'Problem 11009.', The American Mathematical Monthly, 110 341341 (2003) 


2003 
Benoist J, Borwein JM, Popovici N, 'A characterization of quasiconvex vectorvalued functions', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 131 11091113 (2003) [C1]



2003 
Borwein JM, Dontchev AL, 'On the BartleGraves theorem', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 131 25532560 (2003) [C1]



2003 
Borwein J, FItzpatrick S, Girgensohn R, 'Subdifferentials whose graphs are not normxweak* closed', CANADIAN MATHEMATICAL BULLETINBULLETIN CANADIEN DE MATHEMATIQUES, 46 538545 (2003) [C1]



2003 
Bauschke HH, Borwein JM, Combettes PL, 'Bregman monotone optimization algorithms', SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 42 596636 (2003) [C1]



2003 
Borwein JM, Vanderwerff J, Wang XF, 'Local Lipschitzconstant functions and maximal subdifferentials', SETVALUED ANALYSIS, 11 3767 (2003) [C1]



2003 
Borwein J, Choksi R, Marechal P, 'Probability distributions of assets inferred from option prices via the principle of maximum entropy', SIAM JOURNAL ON OPTIMIZATION, 14 464478 (2003) [C1]



2003 
Borwein JM, Goebel R, 'Notions of Relative Interior in Banach spaces', Journal of Mathematical Sciences: a translation of selected Russianlanguage serial publications in mathematics, 115 25422553 (2003) [C1]



2002 
Borwein JM, Fabian M, Loewen PD, 'The range of the gradient of a Lipschitz C1smooth bump in infinite dimensions', ISRAEL JOURNAL OF MATHEMATICS, 132 239251 (2002)



2002 
Borwein JM, JimenezSevilla M, Moreno JP, 'Antiproximinal norms in Banach spaces', JOURNAL OF APPROXIMATION THEORY, 114 5769 (2002)



2002 
Borwein J, Giles J, Vanderwerff J, 'Rotund norms, Clarke subdifferentials and extensions of Lipschitz functions', NONLINEAR ANALYSISTHEORY METHODS & APPLICATIONS, 48 287301 (2002)



2002 
Borwein JM, Zhu QJ, 'A survey of subdifferential calculus with applications (vol 38, pg 687, 1999)', NONLINEAR ANALYSISTHEORY METHODS & APPLICATIONS, 49 295296 (2002)



2002 
Borwein D, Borwein JM, Mares BA, 'Multivariable sinc integrals and volumes of polyhedra', RAMANUJAN JOURNAL, 6 189208 (2002)



2002 
Borwein JM, Vanderwerff JD, 'On the continuity of biconjugate convex functions', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 130 17971803 (2002)



2001 
Borwein JM, 'Generalized trigonometric functions', AMERICAN MATHEMATICAL MONTHLY, 108 473474 (2001) 


2001 
Borwein JM, Bradley DM, Broadhurst DJ, Lisonek P, 'Special values of multiple polylogarithms', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 353 907941 (2001)



2001 
Borwein JM, Moors WB, Wang XF, 'Generalized subdifferentials: A Baire categorical approach', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 353 38753893 (2001)



2001 
Bauschke HH, Borwein JM, Combettes PL, 'Essential smoothness, essential strict convexity, and Legendre functions in Banach spaces', COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 3 615647 (2001)



2001 
Borwein JM, Fitzpatrick SP, 'Duality inequalities and sandwiched functions', NONLINEAR ANALYSISTHEORY METHODS & APPLICATIONS, 46 365380 (2001)



2001 
Borwein J, Kortezov I, 'Some generic results on nonattaining functionals', SETVALUED ANALYSIS, 9 3547 (2001)



2001 
Borwein JM, Vanderwerff JD, 'Convex functions of Legendre type in general Banach spaces', JOURNAL OF CONVEX ANALYSIS, 8 569581 (2001)



2001 
Borwein JM, Broadhurst DJ, Kamnitzer J, 'Central binomial sums, multiple Clausen values, and zeta values', EXPERIMENTAL MATHEMATICS, 10 2534 (2001)



2001 
Borwein D, Borwein J, Fee G, Girgensohn R, 'Refined convexity and special cases of the BlaschkeSantalo inequality', MATHEMATICAL INEQUALITIES & APPLICATIONS, 4 631638 (2001)



2001 
Borwein D, Borwein JM, 'Some remarkable properties of sinc and related integrals', RAMANUJAN JOURNAL, 5 7389 (2001)



2001 
Borwein JM, Borwein PB, 'Challenges in mathematical computing', COMPUTING IN SCIENCE & ENGINEERING, 3 4853 (2001)



2001 
Bauschke HH, Borwein JM, 'Joint and separate convexity of the bregman distance', Studies in Computational Mathematics, 8 2336 (2001)
Algorithms involving Bregman projections for solving optimization problems have beenreceiving much attention lately. Several of these methods rely crucially on the joint convexity... [more]
Algorithms involving Bregman projections for solving optimization problems have beenreceiving much attention lately. Several of these methods rely crucially on the joint convexity of the Bregman distance. In this note, we study joint and separate convexity of Bregman distances. To bring out the main ideas more clearly, we consider first functions defined on an open interval. Our main result states that the Bregman distance of a given function is jointly convex if and only if the reciprocal of its second derivative is concave. We observe that Bregman distances induced by the two most popular choicesthe energy and the BoltzmannShannon entropyare limiting cases in a profound sense. This result is generalized by weakening assumptions on differentiability and strict convexity. We then consider general, not necessarily separable, convex functions. The characterization of joint convexity has a natural and beautiful analog. Finally, we discuss spectral functions, where the situation is less clear. Throughout, we provide numerous examples to illustrate our results. Â© 2001 Elsevier B.V. All rights reserved.



2000 
Borwein JM, Bradley DM, Crandall RE, 'Computational strategies for the Riemann zeta function', JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 121 247296 (2000)



2000 
Borwein J, Lucet Y, Mordukhovich B, 'Compactly epiLipschitzian convex sets and functions in normed spaces', JOURNAL OF CONVEX ANALYSIS, 7 375393 (2000)



2000 
Bauschke HH, Borwein JM, Tseng P, 'Bounded linear regularity, strong CHIP, and CHIP are distinct properties', JOURNAL OF CONVEX ANALYSIS, 7 395412 (2000)



2000 
Borwein J, Choi KKS, 'On the representations of xy plus yz plus zx', EXPERIMENTAL MATHEMATICS, 9 153158 (2000)



2000 
Borwein JM, Marechal P, Naugler D, 'A convex dual approach to the computation of NMR complex spectra', MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 51 91102 (2000)



2000 
Borwein D, Borwein JM, Marechal P, 'Surprise maximization', AMERICAN MATHEMATICAL MONTHLY, 107 517527 (2000)



2000 
Borwein JM, 'Moments of the Poisson distribution', AMERICAN MATHEMATICAL MONTHLY, 107 659659 (2000)



2000 
Borwein JM, Moors WB, 'Separable determination of integrability and minimality of the Clarke subdifferential mapping', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 128 215221 (2000)



2000 
Borwein JM, Wang XF, 'Lipschitz functions with maximal Clarke subdifferentials are generic', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 128 32213229 (2000)



1999 
Borwein JM, Corless RM, 'Emerging tools for experimental mathematics', AMERICAN MATHEMATICAL MONTHLY, 106 889909 (1999)



1999 
Marechal P, Togane D, Celler A, Borwein JM, 'Computation and stability analysis for regularized tomographic reconstructions', IEEE TRANSACTIONS ON NUCLEAR SCIENCE, 46 21772184 (1999)



1999 
Borwein JM, Mordukhovich BS, Shao YH, 'On the equivalence of some basic principles in variational analysis', JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 229 228257 (1999)



1999 
Bauschke HH, Borwein JM, Li W, 'Strong conical hull intersection property, bounded linear regularity, Jameson's property (G), and error bounds in convex optimization', MATHEMATICAL PROGRAMMING, 86 135160 (1999)



1999 
Bauschke HH, Borwein JM, 'Maximal monotonicity of dense type, local maximal monotonicity, and monotonicity of the conjugate are all the same for continuous linear operators', PACIFIC JOURNAL OF MATHEMATICS, 189 120 (1999)



1999 
Bauschke HH, Noll D, Celler A, Borwein JM, 'An EM algorithm for dynamic SPECT', IEEE TRANSACTIONS ON MEDICAL IMAGING, 18 252261 (1999)



1999 
Borwein J, Moors WB, Shao Y, 'Subgradient representation of multifunctions', JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES BAPPLIED MATHEMATICS, 40 301313 (1999)



1999 
Borwein JM, Treiman JS, Zhu QJJ, 'Partially smooth variational principles and applications', NONLINEAR ANALYSISTHEORY METHODS & APPLICATIONS, 35 10311059 (1999)



1999 
Borwein JM, Zhu QJJ, 'A survey of subdifferential calculus with applications', NONLINEAR ANALYSISTHEORY METHODS & APPLICATIONS, 38 687773 (1999)



1999 
Marechal P, Togane D, Celler A, Borwein JM, 'Assessment of the performance of reconstruction processes for computed tomography', IEEE Nuclear Science Symposium and Medical Imaging Conference, 2 13531357 (1999)
This paper deals with the assessment of the performance of reconstruction methods for computed tomography, including Filtered Back Projection and 'entropylike' methods. For each ... [more]
This paper deals with the assessment of the performance of reconstruction methods for computed tomography, including Filtered Back Projection and 'entropylike' methods. For each of these methods, the influence of errors in the measured data on the reconstructed image is analyzed. A small perturbation of the data vector induces a perturbation of the reconstructed object which can be computed by means of the sensitivity matrix. Using appropriate matrix computation techniques, an upper bound on the size of the reconstruction error is determined, as well as the pattern of noise in the sinogram that will result in the largest reconstruction error. Simulations will illustrate our analysis and demonstrate its utility in the interpretation of computed images and in the selection of reconstruction parameters.



1998 
Borwein JM, Wang XF, 'The converse of the mean value theorem may fail generically', AMERICAN MATHEMATICAL MONTHLY, 105 847848 (1998)



1998 
Borwein JM, Treiman JS, Zhu QJ, 'Necessary conditions for constrained optimization problems with semicontinuous and continuous data', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 350 24092429 (1998)



1998 
Borwein D, Borwein JM, Pinner C, 'Convergence of Madelunglike lattice sums', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 350 31313167 (1998)



1998 
Borwein JM, Girgensohn R, Wang XF, 'On the construction of holder and proximal subderivatives', CANADIAN MATHEMATICAL BULLETINBULLETIN CANADIEN DE MATHEMATIQUES, 41 497507 (1998)



1998 
Borwein JM, 'BrouwerHeyting sequences converge', MATHEMATICAL INTELLIGENCER, 20 1415 (1998)



1998 
Borwein JM, Zhu QJ, 'Limiting convex examples for nonconvex subdifferential calculus', Journal of Convex Analysis, 5 221235 (1998)



1998 
Borwein JM, Moors WB, 'A chain rule for essentially smooth Lipschitz functions', SIAM JOURNAL ON OPTIMIZATION, 8 300308 (1998)



1998 
Borwein JM, Moors WB, 'Null sets and essentially smooth Lipschitz functions', SIAM JOURNAL ON OPTIMIZATION, 8 309323 (1998)



1998 
Borwein JM, Bradley DM, Broadhurst DJ, Lisonek P, 'Combinatorial aspects of multiple zeta values', Electronic Journal of Combinatorics, 5 (1998)
Multiple zeta values (MZVs, also called Euler sums or multiple harmonic series) are nested generalizations of the classical Riemann zeta function evaluated at integer values. The ... [more]
Multiple zeta values (MZVs, also called Euler sums or multiple harmonic series) are nested generalizations of the classical Riemann zeta function evaluated at integer values. The fact that an integral representation of MZVs obeys a shuffle product rule allows the possibility of a combinatorial approach to them. Using this approach we prove a longstanding conjecture of Don Zagier about MZVs with certain repeated arguments. We also prove a similar cyclic sum identity. Finally, we present extensive computational evidence supporting an in finite family of conjectured MZV identities that simultaneously generalize the Zagier identity.



1998 
Borwein JM, 'A generalization of Young's l(p) equality', MATHEMATICAL INEQUALITIES & APPLICATIONS, 1 131136 (1998)



1998 
Borwein JM, Jofre A, 'A nonconvex separation property in Banach spaces', MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 48 169179 (1998)



1997 
Borwein J, Monagan M, 'A note from the editors  Winter 1997, Vol 4, No 1', MAPLETECH, 4 11 (1997) 


1997 
Borwein JM, Lisonek P, Macdonald JA, 'Arithmeticgeometric means revisited', MAPLETECH, 4 2027 (1997) 


1997 
Borwein J, Monagan M, 'Differential equations in Maple: A short tutorial', MAPLETECH, 4 5558 (1997) 


1997 
Borwein JM, Bradley DM, Broadhurst DJ, 'Evaluations of kfold Euler/Zagier sums: A compendium of results for arbitrary k', Electronic Journal of Combinatorics, 4 121 (1997)
Euler sums (also called Zagier sums) occur within the context of knot theory and quantum field theory. There are various conjectures related to these sums whose incompletion is a ... [more]
Euler sums (also called Zagier sums) occur within the context of knot theory and quantum field theory. There are various conjectures related to these sums whose incompletion is a sign that both the mathematics and physics communities do not yet completely understand the field. Here, we assemble results for Euler/Zagier sums (also known as multidimensional zeta/harmonic sums) of arbitrary depth, including sign alternations. Many of our results were obtained empirically and are apparently new. By carefully compiling and examining a huge data base of high precision numerical evaluations, we can claim with some confidence that certain classes of results are exhaustive. While many proofs are lacking, we have sketched derivations of all results that have so far been proved.



1997 
Borwein J, Bradley D, 'Empirically determined ApÃ©rylike formulae for Â¿(4n+3)', Experimental Mathematics, 6 181194 (1997)
Some rapidly convergent formulae for special values of the Riemann zeta function are given. We obtain a generating function formula for Â¿(4n+3) that generalizes ApÃ©ry's series f... [more]
Some rapidly convergent formulae for special values of the Riemann zeta function are given. We obtain a generating function formula for Â¿(4n+3) that generalizes ApÃ©ry's series for Â¿(3), and appears to give the best possible series relations of this type, at least for n < 12. The formula reduces to a finite but apparently nontrivial combinatorial identity. The identity is equivalent to an interesting new integral evaluation for the central binomial coefficient. We outline a new technique for transforming and summing certain infinite series. We also derive a formula that provides strange evaluations of a large new class of nonterminating hypergeometric series.



1997 
Borwein JM, Wang XF, 'Distinct differentiable functions may share the same Clarke subdifferential at all points', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 125 807813 (1997)



1997 
Borwein J, Vanderwerff J, 'Convex functions on Banach spaces not containing l(1)', CANADIAN MATHEMATICAL BULLETINBULLETIN CANADIEN DE MATHEMATIQUES, 40 1018 (1997)



1997 
Borwein JM, Moors WB, 'Essentially smooth Lipschitz functions', JOURNAL OF FUNCTIONAL ANALYSIS, 149 305351 (1997)



1997 
Borwein JM, Sun W, 'The stability analysis of dynamic SPECT systems', NUMERISCHE MATHEMATIK, 77 283298 (1997)



1997 
Bailey DH, Borwein JM, Crandall RE, 'On the Khintchine constant', Mathematics of Computation, 66 417431 (1997)



1997 
Bauschke HH, Borwein JM, 'Legendre functions and the method of random bregman projections', Journal of Convex Analysis, 4 2767 (1997)



1997 
Bailey DH, Borwein JM, Borwein PB, Plouffe S, 'The quest for Pi', MATHEMATICAL INTELLIGENCER, 19 5057 (1997)



1997 
Borwein JM, Zhu QJJ, 'Variational analysis in nonreflexive spaces and applications to control problems with L(1) perturbations', NONLINEAR ANALYSISTHEORY METHODS & APPLICATIONS, 28 889915 (1997)



1997 
Borwein JM, Moors WB, Wang XF, 'Lipschitz functions with prescribed derivatives and subderivatives', NONLINEAR ANALYSISTHEORY METHODS & APPLICATIONS, 29 5363 (1997)



1996 
Borwein D, Borwein JM, Borwein PB, Girgensohn R, 'Giuga's conjecture on primality', AMERICAN MATHEMATICAL MONTHLY, 103 4050 (1996)



1996 
Borwein JM, Vanderwerff JD, 'Banach spaces that admit support sets', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 124 751755 (1996)



1996 
Borwein JM, Vanderwerff JD, 'Epigraphical and uniform convergence of convex functions', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 348 16171631 (1996)



1996 
Bauschke HH, Borwein JM, 'Projection algorithms for solving convex feasibility problems', SIAM REVIEW, 38 367426 (1996)



1996 
Borwein J, Borwein P, Girgensohn R, Parnes S, 'Making sense of experimental mathematics', MATHEMATICAL INTELLIGENCER, 18 1218 (1996)



1996 
Borwein JM, Zhu QJ, 'Viscosity solutions and viscosity subderivatives in smooth Banach spaces with applications to metric regularity', SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 34 15681591 (1996)



1996 
Borwein JM, Lewis AS, Noll D, 'Maximum entropy reconstruction using derivative information .1. Fisher information and convex duality', MATHEMATICS OF OPERATIONS RESEARCH, 21 442468 (1996)



1996 
Borwein JM, Ioffe A, 'Proximal analysis in smooth spaces', SETVALUED ANALYSIS, 4 124 (1996)



1996 
Borwein D, Borwein JM, Wang XF, 'Approximate subgradients and coderivatives in R(n)', SETVALUED ANALYSIS, 4 375398 (1996)



1996 
Borwein JM, Girgensohn R, 'Evaluation of triple Euler sums', Electronic Journal of Combinatorics, 3 127 (1996)
Let a, b, c be positive integers and define the socalled triple, double and single Euler sums by Â¿(a, b, c) := Â¿sum;sum; x=1 y=1 z=18; x=1 y=11/xay bzc, Â¿(a, b) := Â¿Â¿x=1 y=1... [more]
Let a, b, c be positive integers and define the socalled triple, double and single Euler sums by Â¿(a, b, c) := Â¿sum;sum; x=1 y=1 z=18; x=1 y=11/xay bzc, Â¿(a, b) := Â¿Â¿x=1 y=18 x=11/xayb and Â¿(a) := Â¿x=181/xa. Extending earlier work about double sums, we prove that whenever a + b + c is even or less than 10, then Â¿(a, b, c) can be expressed as a rational linear combination of products of double and single Euler sums. The proof involves finding and solving linear equations which relate the different types of sums to each other. We also sketch some applications of these results in Theoretical Physics.



1996 
Borwein JM, Corless RM, 'The Encyclopedia of Integer Sequences (N. J. A. Sloane and Simon Plouffe)', SIAM Review, 38 333337 (1996)



1995 
BORWEIN JM, HUANG WZ, 'A FAST HEURISTIC METHOD FOR POLYNOMIAL MOMENT PROBLEMS WITH BOLTZMANNSHANNON ENTROPY', SIAM JOURNAL ON OPTIMIZATION, 5 6899 (1995)



1995 
BORWEIN D, BORWEIN JM, 'ON AN INTRIGUING INTEGRAL AND SOME SERIES RELATED TO ZETA(4)', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 123 11911198 (1995)



1995 
BORWEIN JM, GIRGENSOHN R, 'ADDITION THEOREMS AND BINARY EXPANSIONS', CANADIAN JOURNAL OF MATHEMATICSJOURNAL CANADIEN DE MATHEMATIQUES, 47 262273 (1995)



1995 
BORWEIN D, BORWEIN JM, GIRGENSOHN R, 'EXPLICIT EVALUATION OF EULER SUMS', PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 38 277294 (1995)



1995 
Limber MA, Limber MN, Celler A, Barney JS, Borwein JM, 'Direct Reconstruction of Functional Parameters for Dynamic SPECT', IEEE Transactions on Nuclear Science, 42 12491256 (1995)
We have developed a dynamic SPECT method which allows the prevalent rotating camera systems to be used. In this method, the parameters of the timeactivity curve in each pixel are... [more]
We have developed a dynamic SPECT method which allows the prevalent rotating camera systems to be used. In this method, the parameters of the timeactivity curve in each pixel are recovered directly from the projection data, without first reconstructing a series of static images. Preliminary test results show that we can accurately recover timeactivity curves for a simple model based on activity values expected for myocardial viability studies with fatty acid tracers. Â© 1995 IEEE.



1995 
BORWEIN JM, VANDERWERFF JD, 'CONVERGENCE OF LIPSCHITZ REGULARIZATIONS OF CONVEXFUNCTIONS', JOURNAL OF FUNCTIONAL ANALYSIS, 128 139162 (1995)



1995 
BORWEIN JM, LEWIS AS, LIMBER MN, NOLL D, 'MAXIMUMENTROPY RECONSTRUCTION USING DERIVATIVE INFORMATION .2. COMPUTATIONAL RESULTS', NUMERISCHE MATHEMATIK, 69 243256 (1995)



1994 
Borwein JM, Girgensohn R, 'Functional Equations and Distribution Functions', Results in Mathematics, 26 229237 (1994)
We consider the functional equationwhere 0 < a < 1, b in N {1} and 1 = Ã0 = Ã1 = Â¿ = Ãb 1 =1 are given parameters, Â¿: R Â¿ R is the unknown. We show that there is a unique ... [more]
We consider the functional equationwhere 0 < a < 1, b in N {1} and 1 = Ã0 = Ã1 = Â¿ = Ãb 1 =1 are given parameters, Â¿: R Â¿ R is the unknown. We show that there is a unique bounded function Â¿ which solves (F) and satisfies Â¿(t) = 0 for t < ~1/(1  a), Â¿(t) = 1 for t > 1/(1  a). This solution can be interpreted as the distribution function of a certain random series. It is known to be either singular or absolutely continuous, but the problem for which parameters it is absolutely continuous is largely open. We collect some previously established partial answers and generalize them. We also point out an interesting connection to the socalled Schilling equation. Â© 1994, BirkhÃ¤user Verlag, Basel. All rights reserved.



1994 
BORWEIN JM, HSU LC, MABRY R, NEU K, ROPPERT J, TYLER DB, DEWEGER BMM, 'NEAREST INTEGER ZETAFUNCTIONS', AMERICAN MATHEMATICAL MONTHLY, 101 579580 (1994) 


1994 
BORWEIN JM, NOLL D, '2NDORDER DIFFERENTIABILITY OF CONVEXFUNCTIONS IN BANACHSPACES', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 342 4381 (1994)



1994 
BORWEIN JM, BORWEIN PB, GARVAN FG, 'SOME CUBIC MODULAR IDENTITIES OF RAMANUJAN', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 343 3547 (1994)



1994 
BORWEIN JM, LEWIS AS, LIMBER MA, 'ENTROPY MINIMIZATION WITH LATTICE BOUNDS', JOURNAL OF APPROXIMATION THEORY, 79 116 (1994)



1994 
Bauschke HH, Borwein JM, 'Dykstra's Alternating Projection Algorithm for Two Sets', Journal of Approximation Theory, 79 418443 (1994)



1994 
BORWEIN JM, LEWIS AS, NUSSBAUM RD, 'ENTROPY MINIMIZATION, DAD PROBLEMS, AND DOUBLY STOCHASTIC KERNELS', JOURNAL OF FUNCTIONAL ANALYSIS, 123 264307 (1994)



1994 
BORWEIN JM, FABIAN M, 'A NOTE ON REGULARITY OF SETS AND OF DISTANCE FUNCTIONS IN BANACHSPACE', JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 182 566570 (1994)



1994 
BORWEIN D, BORWEIN JM, 'ON SOME TRIGONOMETRIC AND EXPONENTIAL LATTICE SUMS', JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 188 209218 (1994)



1994 
BORWEIN J, VANDERWERFF J, 'DUAL KADECKLEE NORMS AND THE RELATIONSHIPS BETWEEN WIJSMAN, SLICE, AND MOSCO CONVERGENCE', MICHIGAN MATHEMATICAL JOURNAL, 41 371387 (1994)



1994 
Borwein JM, Huang W, 'Uniform convergence for moment problems with FermiDirac type entropies', ZOR Zeitschrift fÃ¼r Operations Research Mathematical Methods of Operations Research, 40 239252 (1994)



1994 
BORWEIN JM, LEWIS AS, 'STRONG ROTUNDITY AND OPTIMIZATION', SIAM JOURNAL ON OPTIMIZATION, 4 146158 (1994)



1994 
Bailey DH, Borwein JM, Girgensohn R, 'Experimental Evaluation of Euler Sums', Experimental Mathematics, 3 1730 (1994)



1993 
BORWEIN JM, ZHUANG D, 'SUPER EFFICIENCY IN VECTOR OPTIMIZATION', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 338 105122 (1993)



1993 
HIRSCHHORN M, GARVAN F, BORWEIN J, 'CUBIC ANALOGS OF THE JACOBIAN THETAFUNCTION THETA(Z,Q)', CANADIAN JOURNAL OF MATHEMATICSJOURNAL CANADIEN DE MATHEMATIQUES, 45 673694 (1993)



1993 
BORWEIN JM, FABIAN M, 'ON CONVEXFUNCTIONS HAVING POINTS OF GATEAUX DIFFERENTIABILITY WHICH ARE NOT POINTS OF FRECHET DIFFERENTIABILITY', CANADIAN JOURNAL OF MATHEMATICSJOURNAL CANADIEN DE MATHEMATIQUES, 45 11211134 (1993)



1993 
BORWEIN JM, FITZPATRICK S, 'A WEAK HADAMARD SMOOTH RENORMING OF L(1)(NU,MU)', CANADIAN MATHEMATICAL BULLETINBULLETIN CANADIEN DE MATHEMATIQUES, 36 407413 (1993)



1993 
BORWEIN JM, BORWEIN PB, 'INEQUALITIES FOR COMPOUND MEAN ITERATIONS WITH LOGARITHMIC ASYMPTOTES', JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 177 572582 (1993)



1993 
Beer G, Borwein JM, 'Mosco and Slice Convergence of Level Sets and Graphs of Linear Functionals', Journal of Mathematical Analysis and Applications, 175 5367 (1993)



1993 
BORWEIN JM, BORWEIN PB, 'ON THE GENERATING FUNCTION OF THE INTEGER PART  [NALPHA+GAMMA]', JOURNAL OF NUMBER THEORY, 43 293318 (1993)



1993 
BORWEIN JM, 'ON THE FAILURE OF MAXIMUMENTROPY RECONSTRUCTION FOR FREDHOLM EQUATIONS AND OTHER INFINITE SYSTEMS', MATHEMATICAL PROGRAMMING, 61 251261 (1993)



1993 
BORWEIN J, BORWEIN P, 'PI IN THE SKY  COUNTING, THINKING, AND BEING  BARROW,JD', SCIENCE, 259 19281930 (1993)



1993 
BORWEIN J, BORWEIN P, GARVAN F, 'HYPERGEOMETRIC ANALOGS OF THE ARITHMETIC GEOMETRIC MEAN ITERATION', CONSTRUCTIVE APPROXIMATION, 9 509523 (1993)



1993 
BORWEIN JM, FABIAN M, 'ON GENERIC 2NDORDER GATEAUX DIFFERENTIABILITY', NONLINEAR ANALYSISTHEORY METHODS & APPLICATIONS, 20 13731382 (1993)



1993 
BORWEIN JM, BORWEIN PB, 'CLASS NUMBER 3 RAMANUJAN TYPE SERIES FOR 1/PI', JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 46 281290 (1993)



1993 
Bauschke HH, Borwein JM, 'On the convergence of von Neumann's alternating projection algorithm for two sets', SetValued Analysis, 1 185212 (1993)



1993 
Borwein JM, Lewis AS, 'Convergence of decreasing sequences of convex sets in nonreflexive Banach spaces', SetValued Analysis, 1 355363 (1993)



1992 
BORWEIN JM, BORWEIN PB, 'STRANGE SERIES AND HIGHPRECISION FRAUD', AMERICAN MATHEMATICAL MONTHLY, 99 622640 (1992)



1992 
BORWEIN JM, LEWIS AS, 'DECOMPOSITION OF MULTIVARIATE FUNCTIONS', CANADIAN JOURNAL OF MATHEMATICSJOURNAL CANADIEN DE MATHEMATIQUES, 44 463482 (1992)



1992 
BORWEIN JM, THERA M, 'SANDWICH THEOREMS FOR SEMICONTINUOUS OPERATORS', CANADIAN MATHEMATICAL BULLETINBULLETIN CANADIEN DE MATHEMATIQUES, 35 463474 (1992)



1992 
BORWEIN J, REICH S, SHAFRIR I, 'KRASNOSELSKIMANN ITERATIONS IN NORMED SPACES', CANADIAN MATHEMATICAL BULLETINBULLETIN CANADIEN DE MATHEMATIQUES, 35 2128 (1992)



1992 
BORWEIN J, LOU S, 'ASYMPTOTICS OF A SEQUENCE OF WITT VECTORS', JOURNAL OF APPROXIMATION THEORY, 69 326337 (1992)



1992 
BORWEIN JM, LEWIS AS, 'PARTIALLY FINITE CONVEXPROGRAMMING .1. QUASI RELATIVE INTERIORS AND DUALITYTHEORY', MATHEMATICAL PROGRAMMING, 57 1548 (1992)



1992 
BORWEIN JM, LEWIS AS, 'PARTIALLY FINITE CONVEXPROGRAMMING .2. EXPLICIT LATTICE MODELS', MATHEMATICAL PROGRAMMING, 57 4983 (1992)



1992 
BORWEIN JM, ZUCKER IJ, 'FAST EVALUATION OF THE GAMMA FUNCTION FOR SMALL RATIONAL FRACTIONS USING COMPLETE ELLIPTIC INTEGRALS OF THE 1ST KIND', IMA JOURNAL OF NUMERICAL ANALYSIS, 12 519526 (1992)



1991 
BORWEIN JM, DEBARRA G, 'NESTED RADICALS', AMERICAN MATHEMATICAL MONTHLY, 98 735739 (1991)



1991 
BORWEIN JM, BORWEIN PB, 'A CUBIC COUNTERPART OF JACOBIS IDENTITY AND THE AGM', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 323 691701 (1991)



1991 
BORWEIN JM, LEWIS AS, 'ON THE CONVERGENCE OF MOMENT PROBLEMS', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 325 249271 (1991)



1991 
BORWEIN J, FITZPATRICK S, KENDEROV P, 'MINIMAL CONVEX USCOS AND MONOTONEOPERATORS ON SMALL SETS', CANADIAN JOURNAL OF MATHEMATICSJOURNAL CANADIEN DE MATHEMATIQUES, 43 461476 (1991)



1991 
BORWEIN D, BORWEIN J, 'FIXEDPOINT ITERATIONS FOR REAL FUNCTIONS', JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 157 112126 (1991)



1991 
BORWEIN JM, BORWEIN PB, 'THE MAN WHO KNEW INFINITY  A LIFE OF THE INDIAN GENIUS RAMANUJAN  KANIGEL,R', SCIENCE, 253 334335 (1991)



1991 
Borwein JM, Zhuang DM, 'Super efficiency in convex vector optimization', ZOR Zeitschrift fÃ¼r Operations Research Methods and Models of Operations Research, 35 175184 (1991)



1991 
BORWEIN JM, LEWIS AS, 'DUALITY RELATIONSHIPS FOR ENTROPYLIKE MINIMIZATION PROBLEMS', SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 29 325338 (1991)



1990 
BEER G, BORWEIN JM, 'MOSCO CONVERGENCE AND REFLEXIVITY', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 109 427436 (1990)



1990 
BORWEIN JM, BORWEIN PB, 'A REMARKABLE CUBIC MEAN ITERATION', LECTURE NOTES IN MATHEMATICS, 1435 2731 (1990)



1989 
BORWEIN JM, BORWEIN PB, DILCHER K, 'PI, EULER NUMBERS, AND ASYMPTOTIC EXPANSIONS', AMERICAN MATHEMATICAL MONTHLY, 96 681687 (1989)



1989 
BORWEIN JM, BORWEIN PB, BAILEY DH, 'RAMANUJAN, MODULAR EQUATIONS, AND APPROXIMATIONS TO PI OR HOW TO COMPUTE ONE BILLION DIGITS OF PI', AMERICAN MATHEMATICAL MONTHLY, 96 201219 (1989)



1989 
BORWEIN JM, FITZPATRICK S, 'MOSCO CONVERGENCE AND THE KADEC PROPERTY', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 106 843851 (1989)



1989 
BORWEIN J, FITZPATRICK S, 'LOCAL BOUNDEDNESS OF MONOTONEOPERATORS UNDER MINIMAL HYPOTHESES', BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 39 439441 (1989)



1989 
BORWEIN JM, FITZPATRICK S, 'EXISTENCE OF NEAREST POINTS IN BANACHSPACES', CANADIAN JOURNAL OF MATHEMATICSJOURNAL CANADIEN DE MATHEMATIQUES, 41 702720 (1989)



1989 
BORWEIN D, BORWEIN JM, SHAIL R, 'ANALYSIS OF CERTAIN LATTICE SUMS', JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 143 126137 (1989)



1989 
BORWEIN JM, BORWEIN PB, 'ON THE MEAN ITERATION (A,B)[(A+3B/4 SQUARE ROOT AB+B/2)', MATHEMATICS OF COMPUTATION, 53 311326 (1989)



1989 
BORWEIN JM, BORWEIN PB, 'APPROXIMATING PI WITH RAMANUJAN MODULAR EQUATIONS', ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 19 93102 (1989)



1989 
BORWEIN JM, STROJWAS HM, 'THE HYPERTANGENT CONE', NONLINEAR ANALYSISTHEORY METHODS & APPLICATIONS, 13 125144 (1989)



1989 
BORWEIN JM, DEMPSTER MAH, 'THE LINEAR ORDER COMPLEMENTARITYPROBLEM', MATHEMATICS OF OPERATIONS RESEARCH, 14 534558 (1989)



1988 
BORWEIN JM, 'A NATURAL LIMIT', AMERICAN MATHEMATICAL MONTHLY, 95 557558 (1988) 


1988 
BORWEIN JM, ZHUANG DM, 'VERIFIABLE NECESSARY AND SUFFICIENT CONDITIONS FOR OPENNESS AND REGULARITY OF SETVALUED AND SINGLEVALUED MAPS', JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 134 441459 (1988)



1988 
BORWEIN JM, BORWEIN PB, 'ON THE COMPLEXITY OF FAMILIAR FUNCTIONS AND NUMBERS', SIAM REVIEW, 30 589601 (1988)



1988 
BORWEIN JM, BORWEIN PB, 'RAMANUJAN AND PI', SCIENTIFIC AMERICAN, 258 112& (1988)



1988 
BARZILAI J, BORWEIN JM, '2POINT STEP SIZE GRADIENT METHODS', IMA JOURNAL OF NUMERICAL ANALYSIS, 8 141148 (1988)



1988 
BORWEIN D, BORWEIN JM, SHAIL R, ZUCKER IJ, 'ENERGY OF STATIC ELECTRON LATTICES', JOURNAL OF PHYSICS AMATHEMATICAL AND GENERAL, 21 15191531 (1988)



1988 
BENTAL A, BORWEIN JM, TEBOULLE M, 'A DUAL APPROACH TO MULTIDIMENSIONAL LP SPECTRAL ESTIMATION PROBLEMS', SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 26 985996 (1988)



1987 
Borwein JM, Giles JR, 'The proximal normal formula in banach space', Transactions of the American Mathematical Society, 302 371381 (1987)
Approximation by proximal normals to the Clarke generalized subdifferential for a distance function generated by a nonempty closed set and the normal cone to the set generated by ... [more]
Approximation by proximal normals to the Clarke generalized subdifferential for a distance function generated by a nonempty closed set and the normal cone to the set generated by the proximal normals are important tools in nonsmooth analysis. We give simple general versions of such formulae in infinite dimensional Banach spaces which satisfy different geometrical conditions. Our first class, of spaces with uniformly GÃ¢teaux differentiable norm includes the Hilbert space case and the formulae is attained through dense subsets. Our second class, of reflexive Kadec smooth spaces is the most general for which such formulae can be obtained for all nonempty closed sets in the space. Our technique also allows us to establish the existence of solutions for a class of optimization problems substantially extending similar work of Ekeland and Lebourg. Â© 1987 American Mathematical Society.



1987 
BORWEIN JM, BORWEIN PB, 'THE WAY OF ALL MEANS', AMERICAN MATHEMATICAL MONTHLY, 94 519522 (1987)



1987 
BORWEIN JM, 'AUTOMATICCONTINUITY AND OPENNESS OF CONVEX RELATIONS', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 99 4955 (1987)



1987 
BORWEIN JM, GILES J, 'THE PROXIMAL NORMAL FORMULA IN BANACHSPACE', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 302 371381 (1987)



1987 
BORWEIN JM, PREISS D, 'A SMOOTH VARIATIONAL PRINCIPLE WITH APPLICATIONS TO SUBDIFFERENTIABILITY AND TO DIFFERENTIABILITY OF CONVEXFUNCTIONS', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 303 517527 (1987)



1987 
BORWEIN JM, STROJWAS HM, 'PROXIMAL ANALYSIS AND BOUNDARIES OF CLOSEDSETS IN BANACHSPACE .2. APPLICATIONS', CANADIAN JOURNAL OF MATHEMATICSJOURNAL CANADIEN DE MATHEMATIQUES, 39 428472 (1987)



1987 
BORWEIN JM, BORWEIN PB, 'EXPLICIT RAMANUJANTYPE APPROXIMATIONS TO PI OF HIGHORDER', PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCESMATHEMATICAL SCIENCES, 97 5359 (1987)



1987 
BORWEIN JM, 'EPILIPSCHITZLIKE SETS IN BANACHSPACE  THEOREMS AND EXAMPLES', NONLINEAR ANALYSISTHEORY METHODS & APPLICATIONS, 11 12071217 (1987)



1987 
WARD DE, BORWEIN JM, 'NONSMOOTH CALCULUS IN FINITE DIMENSIONS', SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 25 13121340 (1987)



1987 
Giles JR, 'The differentiability of real functions on normed linear space using generalized subgradients', J.Math.Anal. and Appl., 128 512534 (1987)



1986 
JAGERS AA, BORWEIN JM, 'REGULAR N AND 2KNGONS INSCRIBED IN A UNITCIRCLE', AMERICAN MATHEMATICAL MONTHLY, 93 304304 (1986) 


1986 
BORWEIN D, BORWEIN JM, 'A NOTE ON ALTERNATING SERIES IN SEVERAL DIMENSIONS', AMERICAN MATHEMATICAL MONTHLY, 93 531539 (1986)



1986 
BORWEIN JM, BORWEIN PB, 'AN EXPLICIT CUBIC ITERATION ITERATION FOR PI', BIT, 26 123126 (1986)



1986 
BORWEIN JM, STROJWAS HM, 'PROXIMAL ANALYSIS AND BOUNDARIES OF CLOSEDSETS IN BANACHSPACE, .1. THEORY', CANADIAN JOURNAL OF MATHEMATICSJOURNAL CANADIEN DE MATHEMATIQUES, 38 431452 (1986)



1986 
BORWEIN JM, 'PARTIALLY MONOTONEOPERATORS AND THE GENERIC DIFFERENTIABILITY OF CONVEX CONCAVE AND BICONVEX MAPPINGS', ISRAEL JOURNAL OF MATHEMATICS, 54 4250 (1986)



1986 
Borwein JM, 'Norm duality for convex processes and applications', Journal of Optimization Theory and Applications, 48 5364 (1986)



1986 
Borwein JM, 'Stability and regular points of inequality systems', Journal of Optimization Theory and Applications, 48 952 (1986)



1986 
BORWEIN JM, ZHUANG D, 'ON FAN MINIMAX THEOREM', MATHEMATICAL PROGRAMMING, 34 232234 (1986)



1986 
BORWEIN JM, WOLKOWICZ H, 'A SIMPLE CONSTRAINT QUALIFICATION IN INFINITE DIMENSIONAL PROGRAMMING', MATHEMATICAL PROGRAMMING, 35 8396 (1986)



1986 
BORWEIN JM, BORWEIN PB, 'MORE QUADRATICALLY CONVERGING ALGORITHMS FOR PI', MATHEMATICS OF COMPUTATION, 46 247253 (1986)



1986 
BORWEIN JM, 'GENERIC DIFFERENTIABILITY OF ORDERBOUNDED CONVEX OPERATORS', JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES BAPPLIED MATHEMATICS, 28 2229 (1986)



1985 
BORWEIN J, 'AN EXTENSION OF HADAMARD INEQUALITY', AMERICAN MATHEMATICAL MONTHLY, 92 148149 (1985)



1985 
BORWEIN JM, TINGLEY DW, 'ON SUPPORTLESS CONVEXSETS', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 94 471476 (1985)



1985 
BORWEIN J, 'SOME MODULAR IDENTITIES OF RAMANUJAN USEFUL IN APPROXIMATING PI', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 95 365371 (1985)



1985 
BORWEIN D, BORWEIN JM, TAYLOR KF, 'CONVERGENCE OF LATTICE SUMS AND MADELUNG CONSTANT', JOURNAL OF MATHEMATICAL PHYSICS, 26 29993009 (1985)



1985 
BORWEIN JM, 'ALTERNATIVE THEOREMS FOR GENERAL COMPLEMENTARITYPROBLEMS', LECTURE NOTES IN ECONOMICS AND MATHEMATICAL SYSTEMS, 259 194203 (1985)



1985 
BORWEIN JM, STROJWAS HM, 'TANGENTIAL APPROXIMATIONS', NONLINEAR ANALYSISTHEORY METHODS & APPLICATIONS, 9 13471366 (1985)



1984 
BORWEIN JM, SIMS B, 'NONEXPANSIVE MAPPINGS ON BANACHLATTICES AND RELATED TOPICS', HOUSTON JOURNAL OF MATHEMATICS, 10 339356 (1984)



1984 
BORWEIN JM, 'AN INTEGRAL CHARACTERIZATION OF EUCLIDEANSPACE', BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 29 357364 (1984)



1984 
BORWEIN JM, STROJWAS HM, 'DIRECTIONALLY LIPSCHITZIAN MAPPINGS ON BAIRE SPACES', CANADIAN JOURNAL OF MATHEMATICSJOURNAL CANADIEN DE MATHEMATIQUES, 36 95130 (1984)



1984 
BORWEIN JM, RICHMOND B, 'HOW MANY MATRICES HAVE ROOTS', CANADIAN JOURNAL OF MATHEMATICSJOURNAL CANADIEN DE MATHEMATIQUES, 36 286299 (1984)



1984 
BORWEIN JM, BORWEIN PB, 'CUBIC AND HIGHERORDER ALGORITHMS FOR PI', CANADIAN MATHEMATICAL BULLETINBULLETIN CANADIEN DE MATHEMATIQUES, 27 436443 (1984)



1984 
BORWEIN JM, YOST DT, 'ABSOLUTE NORMS ON VECTOR LATTICES', PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 27 215222 (1984)



1984 
Borwein JM, Penot JP, Thera M, 'Conjugate convex operators', Journal of Mathematical Analysis and Applications, 102 399414 (1984)



1984 
BORWEIN JM, 'GENERALIZED LINEAR COMPLEMENTARITYPROBLEMS TREATED WITHOUT FIXEDPOINT THEORY', JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 43 343356 (1984)



1984 
BORWEIN JM, NIEUWENHUIS JW, '2 KINDS OF NORMALITY IN VECTOR OPTIMIZATION', MATHEMATICAL PROGRAMMING, 28 185191 (1984)



1984 
BORWEIN JM, BORWEIN PB, 'THE ARITHMETICGEOMETRIC MEAN AND FAST COMPUTATION OF ELEMENTARYFUNCTIONS', SIAM REVIEW, 26 351366 (1984)



1983 
BORWEIN JM, 'SEMIINFINITE PROGRAMMING DUALITY  HOW SPECIAL IS IT', LECTURE NOTES IN ECONOMICS AND MATHEMATICAL SYSTEMS, 215 1036 (1983)



1983 
BORWEIN JM, 'COMPLETENESS AND THE CONTRACTION PRINCIPLE', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 87 246250 (1983)



1983 
Borwein JM, 'ADJOINT PROCESS DUALITY.', Mathematics of Operations Research, 8 403434 (1983)



1983 
Borwein JM, 'ON THE EXISTENCE OF PARETO EFFICIENT POINTS.', Mathematics of Operations Research, 8 6473 (1983)



1983 
Borwein JM, Borwein PB, 'A very rapidly convergent product expansion for p', BIT, 23 538540 (1983)



1982 
BORWEIN JM, 'ON THE HAHNBANACH EXTENSION PROPERTY', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 86 4246 (1982)



1982 
BORWEIN JM, 'CONTINUITY AND DIFFERENTIABILITY PROPERTIES OF CONVEX OPERATORS', PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 44 420444 (1982)



1982 
BORWEIN JM, 'A NOTE ON THE EXISTENCE OF SUBGRADIENTS', MATHEMATICAL PROGRAMMING, 24 225228 (1982)



1982 
BORWEIN JM, 'A NOTE ON EPSILONSUBGRADIENTS AND MAXIMAL MONOTONICITY', PACIFIC JOURNAL OF MATHEMATICS, 103 307314 (1982)



1982 
BORWEIN JM, STYAN GPH, FOSTER LV, WOLKOWICZ H, 'SOME INEQUALITIES INVOLVING STATISTICAL EXPRESSIONS', SIAM REVIEW, 24 340342 (1982)



1982 
BORWEIN JM, 'NECESSARY AND SUFFICIENT CONDITIONS FOR QUADRATIC MINIMALITY', NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 5 127140 (1982)



1982 
BORWEIN JM, WOLKOWICZ H, 'CHARACTERIZATIONS OF OPTIMALITY WITHOUT CONSTRAINT QUALIFICATION FOR THE ABSTRACT CONVEX PROGRAM', MATHEMATICAL PROGRAMMING STUDY, 19 77100 (1982)



1982 
Borwein JM, 'NOTE ON THE EXISTENCE OF SUBGRADIENTS.', Mathematical Programming, 24 225228 (1982)



1981 
BORWEIN J, WOLKOWICZ H, 'REGULARIZING THE ABSTRACT CONVEX PROGRAM', JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 83 495530 (1981)



1981 
BORWEIN JM, 'THE LIMITING LAGRANGIAN AS A CONSEQUENCE OF HELLY THEOREM', JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 33 497513 (1981)



1981 
BORWEIN JM, 'A LAGRANGE MULTIPLIER THEOREM AND A SANDWICH THEOREM FOR CONVEX RELATIONS', MATHEMATICA SCANDINAVICA, 48 189204 (1981)



1981 
BORWEIN JM, 'DIRECT THEOREMS IN SEMIINFINITE CONVEXPROGRAMMING', MATHEMATICAL PROGRAMMING, 21 301318 (1981)



1981 
BORWEIN JM, WOLKOWICZ H, 'FACIAL REDUCTION FOR A CONECONVEX PROGRAMMING PROBLEM', JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES APURE MATHEMATICS AND STATISTICS, 30 369380 (1981)



1981 
BORWEIN JM, WOLKOWICZ H, 'CHARACTERIZATION OF OPTIMALITY FOR THE ABSTRACT CONVEX PROGRAM WITH FINITE DIMENSIONAL RANGE', JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES APURE MATHEMATICS AND STATISTICS, 30 390411 (1981)



1980 
GRIPENBERG G, WILANSKY A, JOYNER D, ROUSH F, WALSH B, BORWEIN J, 'RANGES IN BANACHSPACES', AMERICAN MATHEMATICAL MONTHLY, 87 6868 (1980) 


1980 
BORWEIN J, KEENER L, 'THE HAUSDORFF METRIC AND CEBYSEV CENTERS', JOURNAL OF APPROXIMATION THEORY, 28 366376 (1980)



1980 
BORWEIN JM, 'LEXICOGRAPHIC MULTIPLIERS', JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 78 309327 (1980)



1980 
BORWEIN JM, 'A STRONG DUALITY THEOREM FOR THE MINIMUM OF A FAMILY OF CONVEXPROGRAMS', JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 31 453472 (1980)



1980 
BORWEIN JM, 'A NOTE ON PERFECT DUALITY AND LIMITING LAGRANGEANS', MATHEMATICAL PROGRAMMING, 18 330337 (1980)



1979 
BORWEIN JM, 'WEAK LOCAL SUPPORTABILITY AND APPLICATIONS TO APPROXIMATION', PACIFIC JOURNAL OF MATHEMATICS, 82 323338 (1979)



1979 
BORWEIN JM, 'MULTIVALUED APPROACH TO THE FARKASLEMMA', MATHEMATICAL PROGRAMMING STUDY, 10 4247 (1979)



1978 
BORWEIN JM, 'STRONGLY EXPOSING FUNCTIONALS', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 69 4648 (1978)



1978 
BORWEIN J, 'WEAK TANGENT CONES AND OPTIMIZATION IN A BANACHSPACE', SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 16 512522 (1978)



1977 
BORWEIN J, EDELSTEIN M, OBRIEN R, 'SOME REMARKS ON VISIBILITY AND STARSHAPE', JOURNAL OF THE LONDON MATHEMATICAL SOCIETYSECOND SERIES, 15 342344 (1977)



1977 
BORWEIN J, 'MULTIVALUED CONVEXITY AND OPTIMIZATION  UNIFIED APPROACH TO INEQUALITY AND EQUALITY CONSTRAINTS', MATHEMATICAL PROGRAMMING, 13 183199 (1977)



1977 
BORWEIN J, 'PROPER EFFICIENT POINTS FOR MAXIMIZATIONS WITH RESPECT TO CONES', SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 15 5763 (1977)



1976 
BORWEIN J, EDELSTEIN M, OBRIEN R, 'VISIBILITY AND STARSHAPE', JOURNAL OF THE LONDON MATHEMATICAL SOCIETYSECOND SERIES, 14 313318 (1976)



1976 
BORWEIN JM, 'FRACTIONAL PROGRAMMING WITHOUT DIFFERENTIABILITY', MATHEMATICAL PROGRAMMING, 11 283290 (1976)


