Ebook: Computational and Analytical Mathematics: In Honor of Jonathan Borwein's 60th Birthday

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.

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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.

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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.

Content:
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