Duality for Nonconvex Approximation and Optimization

Detailed proofs of results are given, along with varied illustrations. While many of the results have been published in mathematical journals, this is the first time these results appear in book form.

Author: Ivan Singer

Publisher: Springer Science & Business Media

ISBN: 9780387283951

Category: Mathematics

Page: 356

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The theory of convex optimization has been constantly developing over the past 30 years. Most recently, many researchers have been studying more complicated classes of problems that still can be studied by means of convex analysis, so-called "anticonvex" and "convex-anticonvex" optimizaton problems. This manuscript contains an exhaustive presentation of the duality for these classes of problems and some of its generalization in the framework of abstract convexity. This manuscript will be of great interest for experts in this and related fields.

Convex Functions

Amer Math. Soc, 13412983I2987, 2006. [396] S. Simons. From HahnIBanach to Monotonicity, volume 1693 of Lecture Notes in ... Duality for Nonconvex Approximation and Optimization, volume 24 of CMS Books in Mathematics/Ouvrages de ...

Author: Jonathan M. Borwein

Publisher: Cambridge University Press

ISBN: 9781139811095

Category: Mathematics

Page:

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Like differentiability, convexity is a natural and powerful property of functions that plays a significant role in many areas of mathematics, both pure and applied. It ties together notions from topology, algebra, geometry and analysis, and is an important tool in optimization, mathematical programming and game theory. This book, which is the product of a collaboration of over 15 years, is unique in that it focuses on convex functions themselves, rather than on convex analysis. The authors explore the various classes and their characteristics and applications, treating convex functions in both Euclidean and Banach spaces. The book can either be read sequentially for a graduate course, or dipped into by researchers and practitioners. Each chapter contains a variety of specific examples, and over 600 exercises are included, ranging in difficulty from early graduate to research level.

Topics in Mathematical Analysis and Applications

Rubinshtein, G.Sh.: Duality in mathematical programming and some problems of convex analysis. Uspekhi Mat. Nauk 25, 5(155), 171–201 (1970) [Russian] 12. Singer, I.: Duality for Nonconvex Approximation and Optimization. CMS Books in ...

Author: Themistocles M. Rassias

Publisher: Springer

ISBN: 9783319065540

Category: Mathematics

Page: 814

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This volume presents significant advances in a number of theories and problems of Mathematical Analysis and its applications in disciplines such as Analytic Inequalities, Operator Theory, Functional Analysis, Approximation Theory, Functional Equations, Differential Equations, Wavelets, Discrete Mathematics and Mechanics. The contributions focus on recent developments and are written by eminent scientists from the international mathematical community. Special emphasis is given to new results that have been obtained in the above mentioned disciplines in which Nonlinear Analysis plays a central role. Some review papers published in this volume will be particularly useful for a broader readership in Mathematical Analysis, as well as for graduate students. An attempt is given to present all subjects in this volume in a unified and self-contained manner, to be particularly useful to the mathematical community.

Convex Analysis and Nonlinear Optimization

CMS Books in Mathematics Ouvrages de mathématiques de la SMC 19 20 21 22 23 24 25 HERMAN/KUCERA/SIMSA Equations and ... Applications SINGER Duality for Nonconvex Approximation and Optimization HIGGINSON/PIMM/SINCLAIR Mathematics and the ...

Author: Jonathan Borwein

Publisher: Springer Science & Business Media

ISBN: 9780387312569

Category: Mathematics

Page: 310

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Optimization is a rich and thriving mathematical discipline, and the underlying theory of current computational optimization techniques grows ever more sophisticated. This book aims to provide a concise, accessible account of convex analysis and its applications and extensions, for a broad audience. Each section concludes with an often extensive set of optional exercises. This new edition adds material on semismooth optimization, as well as several new proofs.

Mathematics and the Aesthetic

... and Their Applications SINGER Duality for Nonconvex Approximation and Optimization SINCLAIR/PIMM/HIGGINSON Mathematics and the Aesthetic William Higginson (Eds.) Mathematics and the Aesthetic New Approaches to CMS Books in Mathematics.

Author: Nathalie Sinclair

Publisher: Springer Science & Business Media

ISBN: 9780387381459

Category: Mathematics

Page: 288

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This collection of essays explores the ancient affinity between the mathematical and the aesthetic, focusing on fundamental connections between these two modes of reasoning and communicating. From historical, philosophical and psychological perspectives, with particular attention to certain mathematical areas such as geometry and analysis, the authors examine ways in which the aesthetic is ever-present in mathematical thinking and contributes to the growth and value of mathematical knowledge.

Convex Functions and their Applications

CMS Books in Mathematics Ouvrages de mathématiques de la SMC 19 20 21 22 23 24 25 1 HERMAN/KUˇCERA/ˇSIMˇSA ... and Their Applications SINGER Duality for Nonconvex Approximation and Optimization HIGGINSON/PIMM/SINCLAIR Mathematics and ...

Author: Constantin Niculescu

Publisher: Springer Science & Business Media

ISBN: 9780387310770

Category: Mathematics

Page: 256

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Thorough introduction to an important area of mathematics Contains recent results Includes many exercises

Handbook of Mathematical Methods in Imaging

Math Annalen 142:291-304 53. Kress R (1999) Linear integral ... Lucchetti R (2006) Convexity and well-posed problems, volume 22 of CMS books in mathematics. ... Singer I (2006) Duality for nonconvex approximation and optimization.

Author: Otmar Scherzer

Publisher: Springer Science & Business Media

ISBN: 9780387929194

Category: Mathematics

Page: 1512

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The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.

Biorthogonal Systems in Banach Spaces

CMS. Books. in. Mathematics. Ouvrages. de. mathématiques ... NICULESCU/PERSSON Convex Functions and Their Applications SINGER Duality for Nonconvex Approximation and Optimization SINCLAIR/PIMM/HIGGINSON Mathematics and the Aesthetic ́ ...

Author: Petr Hajek

Publisher: Springer Science & Business Media

ISBN: 9780387689159

Category: Mathematics

Page: 339

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This book introduces the reader to some of the basic concepts, results and applications of biorthogonal systems in infinite dimensional geometry of Banach spaces, and in topology and nonlinear analysis in Banach spaces. It achieves this in a manner accessible to graduate students and researchers who have a foundation in Banach space theory. The authors have included numerous exercises, as well as open problems that point to possible directions of research.

The Riemann Hypothesis

CMSBooksinMathematics. OuvragesdemathématiquesdelaSMC. 1 Herrman/Kuˇcera/Šimˇsa Equations and Inequalities 2 Arnold Abelian Groups and Representations of Finite Partially Ordered Sets 3 Borwein/Lewis Convex Analysis and Nonlinear ...

Author: Peter B. Borwein

Publisher: Springer Science & Business Media

ISBN: 9780387721255

Category: Mathematics

Page: 533

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The Riemann Hypothesis has become the Holy Grail of mathematics in the century and a half since 1859 when Bernhard Riemann, one of the extraordinary mathematical talents of the 19th century, originally posed the problem. While the problem is notoriously difficult, and complicated even to state carefully, it can be loosely formulated as "the number of integers with an even number of prime factors is the same as the number of integers with an odd number of prime factors." The Hypothesis makes a very precise connection between two seemingly unrelated mathematical objects, namely prime numbers and the zeros of analytic functions. If solved, it would give us profound insight into number theory and, in particular, the nature of prime numbers. This book is an introduction to the theory surrounding the Riemann Hypothesis. Part I serves as a compendium of known results and as a primer for the material presented in the 20 original papers contained in Part II. The original papers place the material into historical context and illustrate the motivations for research on and around the Riemann Hypothesis. Several of these papers focus on computation of the zeta function, while others give proofs of the Prime Number Theorem, since the Prime Number Theorem is so closely connected to the Riemann Hypothesis. The text is suitable for a graduate course or seminar or simply as a reference for anyone interested in this extraordinary conjecture.