Computational and Analytical Mathematics: In Honor of Jonathan Borwein's 60th Birthday (Springer Proceedings in Mathematics & Statistics Book 50)

The research of Jonathan Borwein has had a profound impact on optimization, functional analysis, operations research, mathematical programming, number theory, and experimental mathematics. Having authored more than a dozen books and more than 300 publications, Jonathan Borwein is one of the most productive Canadian mathematicians ever. His research spans pure, applied, and computational mathematics as well as high performance computing, and continues to have an enormous impact: MathSciNet lists more than 2500 citations by more than 1250 authors, and Borwein is one of the 250 most cited mathematicians of the period 1980-1999. He has served the Canadian Mathematics Community through his presidency (2000–02) as well as his 15 years of editing the CMS book series. Jonathan Borwein’s vision and initiative have been crucial in initiating and developing several institutions that provide support for researchers with a wide range of scientific interests. A few notable examples include the Centre for Experimental and Constructive Mathematics and the IRMACS Centre at Simon Fraser University, the Dalhousie Distributed Research Institute at Dalhousie University, the Western Canada Research Grid, and the Centre for Computer Assisted Research Mathematics and its Applications, University of Newcastle. The workshops that were held over the years in Dr. Borwein’s honor attracted high-caliber scientists from a wide range of mathematical fields. This present volume is an outgrowth of the workshop on ‘Computational and Analytical Mathematics’ held in May 2011 in celebration of Dr. Borwein’s 60th Birthday. The collection contains various state-of-the-art research manuscripts and surveys presenting contributions that have risen from the conference, and is an excellent opportunity to survey state-of-the-art research and discuss promising research directions and approaches. 1. Normal numbers and pseudorandom generators / David H. Bailey and Jonathan M. Borwein 2. New demiclosedness principles for (firmly) nonexpansive operators / Heinz H. Bauschke 3. Champernowne's number, strong normality, and the X chromosome / Adrian Belshaw and Peter Borwein 4. Optimality conditions for semivectorial bilevel convex optimal control problems / Henri Bonnel and Jacqueline Morgan 5. Monotone operators without enlargements / Jonathan M. Borwein, Regina S. Burachik and Liangjin Yau 6. A Brøndsted-Rockafellar theorem for diagonal subdifferential operators / Radu Ioan Boţ and Ernö Robert Csetnek 7. A q-analog of Euler's reduction formula for the double Zeta function / David M. Bradley and Xia Zhou 8. Fast computation of Bernoulli, Tangent and Secant numbers / Richard P. Brent and David Harvey 9. Monotone operator methods for Nash equilibria in non-potential games / Luis M. Briceño-Arias and Patrick L. Combettes ^ 10. Compactness, optimality, and risk / B. Cascales, J. Orihuela and M. Ruiz Galán 11. Logarithmic and complex constant term identities /Tom Chappell, Alain Lascoux , S. Ole Warnaar and Wadim Zudilin 12. Preprocessing and regularization for degenerate semidefinite programs / Yuen-Lam Cheung, Simon Schurr and Henry Wolkowicz 13. The largest roots of the Mandelbrot polynomials / Robert M. Corless and Piers W. Lawrence 14. On the fractal distribution of brain synapses / Richard Crandall 15. Visible points in convex sets and best approximation / Frank Deutsch, Hein Hundal and Ludmil Zikatanov 16. On derivative criteria for metric regularity / Asen L. Dontchev and Hélène Frankowska 17. Five classes of monotone linear relations and operators / Mclean R. Edwards 18. Upper semicontinuity of duality and preduality mappings / J.R. Giles 19. Convexity and variational analysis / A.D. Ioffe ^ 20. Generic existence of solutions and generic well-posedness of optimization problems / P.S. Kenderov and J.P. Revalski 21. Legendre functions whose gradients map convex sets to convex sets / Alexander Knecht and Jon Vanderwerff 22. On the convergence of iteration processes for semigroups of nonlinear mappings in Banach spaces / W.M. Kozlowski and Brailey Sims 23. Techniques and open questions in computational convex analysis / Yves Lucet 24. Existence and approximation of fixed points of right Bregman nonexpansive operators / Victoria Martín-Márquez, Simeon Reich and Shoham Sabach 25. Primal lower nice functions and their Moreau envelopes / Marc Mazade and Lionel Thibault 26. Bundle method for non-convex minimization with inexact subgradients and function values / Dominikus Noll 27. Convergence of linesearch and trust-region methods using the Kurdyka-Łojasiewicz inequality / Dominikus Noll and Aude Rondepierre ^ 28. Strong duality in conic linear programming: facial reduction and extended duals / Gábor Pataki 29. Towards a new era in subdifferential analysis? / Jean-Paul Penot 30. Modular equations and lattice sums / Mathew Rogers and Boonrod Yuttanan 31. An epigraph-based approach to sensitivity analysis in set-valued optimization / Douglas E. Ward and Stephen E. Wright. Front Matter....Pages i-xv Normal Numbers and Pseudorandom Generators....Pages 1-18 New Demiclosedness Principles for (Firmly) Nonexpansive Operators....Pages 19-28 Champernowne’s Number, Strong Normality, and the X Chromosome....Pages 29-44 Optimality Conditions for Semivectorial Bilevel Convex Optimal Control Problems....Pages 45-78 Monotone Operators Without Enlargements....Pages 79-103 A Brøndsted–Rockafellar Theorem for Diagonal Subdifferential Operators....Pages 105-112 A q -Analog of Euler’s Reduction Formula for the Double Zeta Function....Pages 113-126 Fast Computation of Bernoulli, Tangent and Secant Numbers....Pages 127-142 Monotone Operator Methods for Nash Equilibria in Non-potential Games....Pages 143-159 Compactness, Optimality, and Risk....Pages 161-218 Logarithmic and Complex Constant Term Identities....Pages 219-250 Preprocessing and Regularization for Degenerate Semidefinite Programs....Pages 251-303 The Largest Roots of the Mandelbrot Polynomials....Pages 305-324 On the Fractal Distribution of Brain Synapses....Pages 325-348 Visible Points in Convex Sets and Best Approximation....Pages 349-364 On Derivative Criteria for Metric Regularity....Pages 365-374 Five Classes of Monotone Linear Relations and Operators....Pages 375-400 Upper Semicontinuity of Duality and Preduality Mappings....Pages 401-410 Convexity and Variational Analysis....Pages 411-444 Generic Existence of Solutions and Generic Well-Posedness of Optimization Problems....Pages 445-453 Legendre Functions Whose Gradients Map Convex Sets to Convex Sets....Pages 455-462 On the Convergence of Iteration Processes for Semigroups of Nonlinear Mappings in Banach Spaces....Pages 463-484 Techniques and Open Questions in Computational Convex Analysis....Pages 485-500 Existence and Approximation of Fixed Points of Right Bregman Nonexpansive Operators....Pages 501-520 Primal Lower Nice Functions and Their Moreau Envelopes....Pages 521-553 Bundle Method for Non-Convex Minimization with Inexact Subgradients and Function Values....Pages 555-592 Convergence of Linesearch and Trust-Region Methods Using the Kurdyka–Łojasiewicz Inequality....Pages 593-611 Strong Duality in Conic Linear Programming: Facial Reduction and Extended Duals....Pages 613-634 Towards a New Era in Subdifferential Analysis?....Pages 635-665 Modular Equations and Lattice Sums....Pages 667-680 An Epigraph-Based Approach to Sensitivity Analysis in Set-Valued Optimization....Pages 681-701 The research of Jonathan Borwein has had a profound impact on optimization, functional analysis, operations research, mathematical programming, number theory, and experimental mathematics. Having authored more than a dozen books and more than 300 publications, Dr. Borwein is one of the most productive Canadian mathematicians ever. His research spans pure, applied, and computational mathematics as well as high performance computing, and continues to have an enormous impact: MathSciNet lists more than 2500 citations by more than 1250 authors, and Borwein is one of the 250 most cited mathematicians of the period 1980–1999. He has served the Canadian Mathematics Community through his presidency (2000–2002) as well as his 15 years of editing the CMS book series. Jonathan Borwein’s vision and initiative have been crucial in initiating and developing several institutions that provide support for researchers with a wide range of scientific interests. A few notable examples include the Centre for Experimental and Constructive Mathematics and the IRMACS Centre at Simon Fraser University, the Dalhousie Distributed Research Institute at Dalhousie University, the Western Canada Research Grid, and the Centre for Computer Assisted Research Mathematics and its Applications, University of Newcastle. The workshops that were held over the years in Dr. Borwein’s honor attracted high-caliber scientists from a wide range of mathematical fields. This present volume is an outgrowth of the workshop entitled ‘Computational and Analytical Mathematics,’ held in May 2011 in celebration of Jonathan Borwein’s 60th Birthday. The collection contains various state-of-the-art research manuscripts and surveys presenting contributions that have risen from the conference, and is an excellent opportunity to survey state-of-the-art research and discuss promising research directions and approaches. The research of Jonathan Borwein has had a profound impact on optimization, functional analysis, operations research, mathematical programming, number theory, and experimental mathematics. Having authored more than a dozen books and more than 300 publications, Dr. Borwein is one of the most productive Canadian mathematicians ever. His research spans pure, applied, and computational mathematics as well as high performance computing, and continues to have an enormous impact: MathSciNet lists more than 2500 citations by more than 1250 authors, and Borwein is one of the 250 most cited mathematicians of the period 1980 1999. He has served the Canadian Mathematics Community through his presidency (2000 2002) as well as his 15 years of editing the CMS book series. Jonathan Borwein's vision and initiative have been crucial in initiating and developing several institutions that provide support for researchers with a wide range of scientific interests. A few notable examples include the Centre for Experimental and Constructive Mathematics and the IRMACS Centre at Simon Fraser University, the Dalhousie Distributed Research Institute at Dalhousie University, the Western Canada Research Grid, and the Centre for Computer Assisted Research Mathematics and its Applications, University of Newcastle. The workshops that were held over the years in Dr. Borwein's honor attracted high-caliber scientists from a wide range of mathematical fields. This present volume is an outgrowth of the workshop entitled Computational and Analytical Mathematics, held in May 2011 in celebration of Jonathan Borwein's 60th Birthday. The collection contains various state-of-the-art research manuscripts and surveys presenting contributions that have risen from the conference, and is an excellent opportunity to survey state-of-the-art research and discuss promising research directions and approaches