Jonathan M. Borwein

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http://www.cs.dal.ca/cspeople/j_borwein.shtml

Articles in Scholarly Journals [Incomplete List]

  1. The evaluation of character Euler double sums
    The Ramanujan Journal, vol. 15, no. 3, pp. 377–405, 2008
  2. The evaluation of Bessel functions via exp-arc integrals
    Journal of Mathematical Analysis and Applications, vol. 341, no. 1, pp. 478–500, 2008
  3. Second Order Cones for Maximal Monotone Operators via Representative Functions
    Set-Valued Analysis, 2008
  4. On the dynamics of certain recurrence relations
    The Ramanujan Journal, vol. 13, no. 1-3, pp. 63–101, 2007
  5. Fitzpatrick functions, cyclic monotonicity and Rockafellar’s antiderivative
    Nonlinear Analysis, vol. 66, no. 5, pp. 1198–1223, 2007
  6. Box integrals
    Journal of Computational and Applied Mathematics, vol. 206, no. 1, pp. 196–208, 2007
  7. Integer Powers of Arcsin
    International Journal of Mathematics and Mathematical Sciences, vol. 2007, Article ID 19381, 10 pages, 2007
  8. Proceedings of the American Mathematical Society, vol. 134, no. 10, pp. 2951–2956, 2006
  9. Integrals of the Ising class
    Journal of Physics A: Mathematical and General, vol. 39, no. 40, pp. 12271–12302, 2006
  10. International Journal of Number Theory, vol. 2, no. 1, p. 65, 2006
  11. Parametric Euler sum identities
    Journal of Mathematical Analysis and Applications, vol. 316, no. 1, pp. 328–338, 2006
  12. Variational Methods in Convex Analysis
    Journal of Global Optimization, vol. 35, no. 2, pp. 197–213, 2006
  13. The Experimental Mathematician: the Pleasure of Discovery and the Role of Proof
    International Journal of Computers for Mathematical Learning, vol. 10, no. 2, pp. 75–108, 2005
  14. Evaluations of binomial series
    Aequationes mathematicae, vol. 70, no. 1-2, pp. 25–36, 2005
  15. Dynamics of a continued fraction of Ramanujan with random coefficients
    Abstract and Applied Analysis, vol. 2005, no. 5, pp. 449–467, 2005
  16. Constructible Convex Sets
    Set-Valued Analysis, vol. 12, no. 1/2, pp. 61–77, 2004
  17. A One Perturbation Variational Principle and Applications
    Set-Valued Analysis, vol. 12, no. 1/2, pp. 49–60, 2004
  18. Proceedings of the American Mathematical Society, vol. 132, no. 04, pp. 1067–1077, 2004
  19. Journal of Mathematical Sciences, vol. 115, no. 4, pp. 2542–2553, 2003
  20. The Ramanujan Journal, vol. 7, no. 1/3, pp. 95–127, 2003
  21. Proceedings of the American Mathematical Society, vol. 131, no. 04, pp. 1109–1114, 2003
  22. Proceedings of the American Mathematical Society, vol. 131, no. 08, pp. 2553–2561, 2003
  23. Set-Valued Analysis, vol. 11, no. 1, pp. 37–67, 2003
  24. Bregman Monotone Optimization Algorithms
    SIAM Journal on Control and Optimization, vol. 42, no. 2, p. 596, 2003
  25. Probability Distributions of Assets Inferred from Option Prices via the Principle of Maximum Entropy
    SIAM Journal on Optimization, vol. 14, no. 2, p. 464, 2003
  26. Proceedings of the American Mathematical Society, vol. 130, no. 06, pp. 1797–1804, 2002
  27. The Ramanujan Journal, vol. 6, no. 2, pp. 189–208, 2002
  28. A survey of subdifferential calculus with applications [Nonlinear Anal. TMA 38 (1999) 687–773]
    Nonlinear Analysis, vol. 49, no. 2, pp. 295–296, 2002
  29. The range of the gradient of a LipschitzC 1-smooth bump in infinite dimensions
    Israel Journal of Mathematics, vol. 132, no. 1, pp. 239–251, 2002
  30. Rotund norms, Clarke subdifferentials and extensions of Lipschitz functions
    Nonlinear Analysis, vol. 48, no. 2, pp. 287–301, 2002
  31. Antiproximinal Norms in Banach Spaces,
    Journal of Approximation Theory, vol. 114, no. 1, pp. 57–69, 2002
  32. Duality inequalities and sandwiched functions
    Nonlinear Analysis, vol. 46, no. 3, pp. 365–380, 2001
  33. Set-Valued Analysis, vol. 9, no. 1/2, pp. 35–47, 2001
  34. The Ramanujan Journal, vol. 5, no. 1, pp. 73–89, 2001
  35. Challenges in mathematical computing
    Computing in Science & Engineering, vol. 3, no. 3, pp. 48–53, 2001
  36. Transactions of the American Mathematical Society, vol. 353, no. 03, pp. 907–942, 2001
  37. Transactions of the American Mathematical Society, vol. 353, no. 10, pp. 3875–3894, 2001
  38. Communications in Contemporary Mathematics, vol. 3, no. 4, p. 615, 2001
  39. Proceedings of the American Mathematical Society, vol. 128, no. 01, pp. 215–222, 2000
  40. Applications of integer relation algorithms
    Discrete Mathematics, vol. 217, no. 1-3, pp. 65–82, 2000
  41. Computational strategies for the Riemann zeta function
    Journal of Computational and Applied Mathematics, vol. 121, no. 1-2, pp. 247–296, 2000
  42. Proceedings of the American Mathematical Society, vol. 128, no. 11, pp. 3221–3230, 2000
  43. A convex dual approach to the computation of NMR complex spectra
    Mathematical Methods of Operations Research (ZOR), vol. 51, no. 1, pp. 91–102, 2000
  44. Surprise Maximization
    The American Mathematical Monthly, vol. 107, no. 6, p. 517, 2000
  45. Emerging Tools for Experimental Mathematics
    The American Mathematical Monthly, vol. 106, no. 10, p. 889, 1999
  46. On the Equivalence of Some Basic Principles in Variational Analysis
    Journal of Mathematical Analysis and Applications, vol. 229, no. 1, pp. 228–257, 1999
  47. Partially smooth variational principles and applications
    Nonlinear Analysis, vol. 35, no. 8, pp. 1031–1059, 1999
  48. A survey of subdifferential calculus with applications
    Nonlinear Analysis, vol. 38, no. 6, pp. 687–773, 1999
  49. Strong conical hull intersection property, bounded linear regularity, Jameson's property (G), and error bounds in convex optimization
    Mathematical Programming, vol. 86, no. 1, pp. 135–160, 1999
  50. Computation and stability analysis for regularized tomographic reconstructions
    IEEE Transactions on Nuclear Science, vol. 46, no. 6, pp. 2177–2184, 1999
  51. A Chain Rule for Essentially Smooth Lipschitz Functions
    SIAM Journal on Optimization, vol. 8, no. 2, p. 300, 1998
  52. Transactions of the American Mathematical Society, vol. 350, no. 08, pp. 3131–3168, 1998
  53. Null Sets and Essentially Smooth Lipschitz Functions
    SIAM Journal on Optimization, vol. 8, no. 2, p. 309, 1998
  54. The Converse of the Mean Value Theorem May Fail Generically
    The American Mathematical Monthly, vol. 105, no. 9, p. 847, 1998
  55. Transactions of the American Mathematical Society, vol. 350, no. 06, pp. 2409–2430, 1998
  56. A nonconvex separation property in Banach spaces
    Mathematical Methods of Operations Research (ZOR), vol. 48, no. 2, pp. 169–179, 1998
  57. The stability analysis of dynamic SPECT systems
    Numerische Mathematik, vol. 77, no. 3, pp. 283–298, 1997
  58. Variational analysis in nonreflexive spaces and applications to control problems with perturbations
    Nonlinear Analysis, vol. 28, no. 5, pp. 889–915, 1997
  59. Lipschitz functions with prescribed derivatives and subderivatives
    Nonlinear Analysis, vol. 29, no. 1, pp. 53–63, 1997
  60. Essentially Smooth Lipschitz Functions
    Journal of Functional Analysis, vol. 149, no. 2, pp. 305–351, 1997
  61. Mathematics of Computation of the American Mathematical Society, vol. 66, no. 217, pp. 417–432, 1997
  62. Proceedings of the American Mathematical Society, vol. 125, no. 03, pp. 807–814, 1997
  63. Proceedings of the American Mathematical Society, vol. 124, no. 03, pp. 751–756, 1996
  64. Viscosity Solutions and Viscosity Subderivatives in Smooth Banach Spaces with Applications to Metric Regularity
    SIAM Journal on Control and Optimization, vol. 34, no. 5, p. 1568, 1996
  65. On Projection Algorithms for Solving Convex Feasibility Problems
    SIAM Review, vol. 38, no. 3, p. 367, 1996
  66. Transactions of the American Mathematical Society, vol. 348, no. 04, pp. 1617–1632, 1996
  67. Approximate subgradients and coderivatives in R n
    Set-Valued Analysis, vol. 4, no. 4, pp. 375–398, 1996
  68. Proximal analysis in smooth spaces
    Set-Valued Analysis, vol. 4, no. 1, pp. 1–24, 1996
  69. Giuga's Conjecture on Primality
    The American Mathematical Monthly, vol. 103, no. 1, p. 40, 1996
  70. On an Intriguing Integral and Some Series Related to ζ(4)
    Proceedings of the American Mathematical Society, vol. 123, no. 4, p. 1191, 1995
  71. Convergence of Lipschitz Regularizations of Convex Functions
    Journal of Functional Analysis, vol. 128, no. 1, pp. 139–162, 1995
  72. Maximum entropy reconstruction using derivative information part 2: computational results
    Numerische Mathematik, vol. 69, no. 3, pp. 243–256, 1995
  73. Direct reconstruction of functional parameters for dynamic SPECT
    IEEE Transactions on Nuclear Science, vol. 42, no. 4, pp. 1249–1256, 1995
  74. Fast heuristic methods for function reconstruction using derivative information
    Applicable Analysis, vol. 58, no. 3, pp. 241–261, 1995
  75. SIAM Journal on Optimization, vol. 5, no. 1, Article ID 0805004, 1995
  76. SIAM Journal on Optimization, vol. 4, no. 1, Article ID 0804008, 1994
  77. Entropy Minimization, DAD Problems, and Doubly Stochastic Kernels
    Journal of Functional Analysis, vol. 123, no. 2, pp. 264–307, 1994
  78. Further arguments for slice convergence in nonreflexive spaces
    Set-Valued Analysis, vol. 2, no. 4, pp. 529–544, 1994
  79. A Note on Regularity of Sets and of Distance Functions in Banach Space
    Journal of Mathematical Analysis and Applications, vol. 182, no. 2, pp. 566–570, 1994
  80. On Some Trigonometric and Exponential Lattice Sums
    Journal of Mathematical Analysis and Applications, vol. 188, no. 1, pp. 209–218, 1994
  81. Dykstra′s Alternating Projection Algorithm for Two Sets
    Journal of Approximation Theory, vol. 79, no. 3, pp. 418–443, 1994
  82. Entropy Minimization with Lattice Bounds
    Journal of Approximation Theory, vol. 79, no. 1, pp. 1–16, 1994
  83. Uniform convergence for moment problems with Fermi-Dirac type entropies
    ZOR Zeitschrift f�r Operations Research Mathematical Methods of Operations Research, vol. 40, no. 3, pp. 239–252, 1994
  84. Second Order Differentiability of Convex Functions in Banach Spaces
    Transactions of the American Mathematical Society, vol. 342, no. 1, p. 43, 1994
  85. Some Cubic Modular Identities of Ramanujan
    Transactions of the American Mathematical Society, vol. 343, no. 1, p. 35, 1994
  86. Super Efficiency in Vector Optimization
    Transactions of the American Mathematical Society, vol. 338, no. 1, p. 105, 1993
  87. Convergence of decreasing sequences of convex sets in nonreflexive Banach spaces
    Set-Valued Analysis, vol. 1, no. 4, pp. 355–363, 1993
  88. On the Generating Function of the Integer Part: [nα + γ]
    Journal of Number Theory, vol. 43, no. 3, pp. 293–318, 1993
  89. Mosco and Slice Convergence of Level Sets and Graphs of Linear Functionals
    Journal of Mathematical Analysis and Applications, vol. 175, no. 1, pp. 53–67, 1993
  90. Class number three Ramanujan type series for 1/π
    Journal of Computational and Applied Mathematics, vol. 46, no. 1-2, pp. 281–290, 1993
  91. On the convergence of von Neumann's alternating projection algorithm for two sets
    Set-Valued Analysis, vol. 1, no. 2, pp. 185–212, 1993
  92. Hypergeometric analogues of the arithmetic-geometric mean iteration
    Constructive Approximation, vol. 9, no. 4, pp. 509–523, 1993
  93. Inequalities for Compound Mean Iterations with Logarithmic Asymptotes
    Journal of Mathematical Analysis and Applications, vol. 177, no. 2, pp. 572–582, 1993
  94. On the failure of maximum entropy reconstruction for Fredholm equations and other infinite systems
    Mathematical Programming, vol. 61, no. 1-3, pp. 251–261, 1993
  95. On generic second-order gateaux differentiability
    Nonlinear Analysis, vol. 20, no. 12, pp. 1373–1382, 1993
  96. SIAM Journal on Optimization, vol. 3, no. 2, Article ID 0803012, 1993
  97. Strange Series and High Precision Fraud
    The American Mathematical Monthly, vol. 99, no. 7, p. 622, 1992
  98. Partially finite convex programming, Part I: Quasi relative interiors and duality theory
    Mathematical Programming, vol. 57, no. 1-3, pp. 15–48, 1992
  99. Partially finite convex programming, Part II: Explicit lattice models
    Mathematical Programming, vol. 57, no. 1-3, pp. 49–83, 1992
  100. Asymptotics of a sequence of Witt vectors
    Journal of Approximation Theory, vol. 69, no. 3, pp. 326–337, 1992
  101. Super efficiency in convex vector optimization
    ZOR Zeitschrift f�r Operations Research Methods and Models of Operations Research, vol. 35, no. 3, pp. 175–184, 1991
  102. Fixed point iterations for real functions
    Journal of Mathematical Analysis and Applications, vol. 157, no. 1, pp. 112–126, 1991
  103. A Cubic Counterpart of Jacobi's Identity and the AGM
    Transactions of the American Mathematical Society, vol. 323, no. 2, p. 691, 1991
  104. SIAM Journal on Optimization, vol. 1, no. 2, Article ID 0801014, 1991
  105. On the Convergence of Moment Problems
    Transactions of the American Mathematical Society, vol. 325, no. 1, p. 249, 1991
  106. Duality Relationships for Entropy-Like Minimization Problems
    SIAM Journal on Control and Optimization, vol. 29, no. 2, p. 325, 1991
  107. Nested Radicals
    The American Mathematical Monthly, vol. 98, no. 8, p. 735, 1991
  108. Mosco Convergence and Reflexivity
    Proceedings of the American Mathematical Society, vol. 109, no. 2, p. 427, 1990
  109. Pi, Euler Numbers, and Asymptotic Expansions
    The American Mathematical Monthly, vol. 96, no. 8, p. 681, 1989
  110. Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi
    The American Mathematical Monthly, vol. 96, no. 3, p. 201, 1989
  111. Mosco Convergence and the Kadec Property
    Proceedings of the American Mathematical Society, vol. 106, no. 3, p. 843, 1989
  112. On the Mean Iteration (a, b) ← � � a+3b 4 , √ab+b 2 � �
    Mathematics of Computation, vol. 53, no. 187, p. 311, 1989
  113. Analysis of certain lattice sums1
    Journal of Mathematical Analysis and Applications, vol. 143, no. 1, pp. 126–137, 1989
  114. The hypertangent cone
    Nonlinear Analysis, vol. 13, no. 2, pp. 125–144, 1989
  115. Verifiable necessary and sufficient conditions for openness and regularity of set-valued and single-valued maps
    Journal of Mathematical Analysis and Applications, vol. 134, no. 2, pp. 441–459, 1988
  116. SIAM Journal on Control and Optimization, vol. 26, no. 4, Article ID 0326053, 1988
  117. SIAM Review, vol. 30, no. 4, Article ID 1030134, 1988
  118. Journal of Physics A: Mathematical and General, vol. 21, no. 7, pp. 1519–1531, 1988
  119. A Smooth Variational Principle With Applications to Subdifferentiability and to Differentiability of Convex Functions
    Transactions of the American Mathematical Society, vol. 303, no. 2, p. 517, 1987
  120. SIAM Journal on Control and Optimization, vol. 25, no. 5, Article ID 0325072, 1987
  121. Epi-Lipschitz-like sets in Banach space: theorems and examples
    Nonlinear Analysis, vol. 11, no. 10, pp. 1207–1217, 1987
  122. The differentiability of real functions on normed linear space using generalized subgradients*1
    Journal of Mathematical Analysis and Applications, vol. 128, no. 2, pp. 512–534, 1987
  123. Automatic Continuity and Openness of Convex Relations
    Proceedings of the American Mathematical Society, vol. 99, no. 1, p. 49, 1987
  124. The Proximal Normal Formula in Banach Space
    Transactions of the American Mathematical Society, vol. 302, no. 1, p. 371, 1987
  125. A Note on Alternating Series in Several Dimensions
    The American Mathematical Monthly, vol. 93, no. 7, p. 531, 1986
  126. On Fan's minimax theorem
    Mathematical Programming, vol. 34, no. 2, pp. 232–234, 1986
  127. A simple constraint qualification in infinite dimensional programming
    Mathematical Programming, vol. 35, no. 1, pp. 83–96, 1986
  128. An explicit cubic iteration for π
    BIT, vol. 26, no. 1, pp. 123–126, 1986
  129. More Quadratically Converging Algorithms for π
    Mathematics of Computation, vol. 46, no. 173, p. 247, 1986
  130. Convergence of lattice sums and Madelung’s constant
    Journal of Mathematical Physics, vol. 26, no. 11, p. 2999, 1985
  131. Tangential approximations
    Nonlinear Analysis, vol. 9, no. 12, pp. 1347–1366, 1985
  132. Some Modular Identities of Ramanujan useful in Approximating π
    Proceedings of the American Mathematical Society, vol. 95, no. 3, p. 365, 1985
  133. On Supportless Convex Sets
    Proceedings of the American Mathematical Society, vol. 94, no. 3, p. 471, 1985
  134. Generalized linear complementarity problems treated without fixed-point theory
    Journal of Optimization Theory and Applications, vol. 43, no. 3, pp. 343–356, 1984
  135. Conjugate convex operators
    Journal of Mathematical Analysis and Applications, vol. 102, no. 2, pp. 399–414, 1984
  136. Two kinds of normality in vector optimization
    Mathematical Programming, vol. 28, no. 2, pp. 185–191, 1984
  137. SIAM Review, vol. 26, no. 3, Article ID 1026073, 1984
  138. Completeness and the Contraction Principle
    Proceedings of the American Mathematical Society, vol. 87, no. 2, p. 246, 1983
  139. A very rapidly convergent product expansion for π
    BIT, vol. 23, no. 4, pp. 538–540, 1983
  140. A note on the existence of subgradients
    Mathematical Programming, vol. 24, no. 1, pp. 225–228, 1982
  141. On the Hahn-Banach Extension Property
    Proceedings of the American Mathematical Society, vol. 86, no. 1, p. 42, 1982
  142. Necessary and sufficient conditions for quadratic minimality
    Numerical Functional Analysis and Optimization, vol. 5, no. 2, pp. 127–140, 1982
  143. Direct theorems in semi-infinite convex programming
    Mathematical Programming, vol. 21, no. 1, pp. 301–318, 1981
  144. Regularizing the abstract convex program*1, *2
    Journal of Mathematical Analysis and Applications, vol. 83, no. 2, pp. 495–530, 1981
  145. The limiting Lagrangian as a consequence of Helly's theorem
    Journal of Optimization Theory and Applications, vol. 33, no. 4, pp. 497–513, 1981
  146. A strong duality theorem for the minimum of a family of convex programs
    Journal of Optimization Theory and Applications, vol. 31, no. 4, pp. 453–472, 1980
  147. Lexicographic multipliers1
    Journal of Mathematical Analysis and Applications, vol. 78, no. 1, pp. 309–327, 1980
  148. A note on perfect duality and limiting lagrangeans
    Mathematical Programming, vol. 18, no. 1, pp. 330–337, 1980
  149. The Hausdorff metric and ebyev centres
    Journal of Approximation Theory, vol. 28, no. 4, pp. 366–376, 1980
  150. SIAM Journal on Control and Optimization, vol. 16, no. 3, Article ID 0316034, 1978
  151. On Strongly Exposing Functionals
    Proceedings of the American Mathematical Society, vol. 69, no. 1, p. 46, 1978
  152. Tangent cones, starshape and convexity
    International Journal of Mathematics and Mathematical Sciences, vol. 1, no. 4, pp. 459–477, 1978
  153. SIAM Journal on Control and Optimization, vol. 15, no. 1, Article ID 0315004, 1977
  154. Multivalued convexity and optimization: A unified approach to inequality and equality constraints
    Mathematical Programming, vol. 13, no. 1, pp. 183–199, 1977
  155. Fractional programming without differentiability
    Mathematical Programming, vol. 11, no. 1, pp. 283–290, 1976