Vector Optimization And Monotone Operators Via Convex Duality PDF Download
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Author | : Sorin-Mihai Grad |
Publisher | : Springer |
Total Pages | : 282 |
Release | : 2014-09-03 |
Genre | : Business & Economics |
ISBN | : 3319089005 |
Download Vector Optimization and Monotone Operators via Convex Duality Book in PDF, ePub and Kindle
This book investigates several duality approaches for vector optimization problems, while also comparing them. Special attention is paid to duality for linear vector optimization problems, for which a vector dual that avoids the shortcomings of the classical ones is proposed. Moreover, the book addresses different efficiency concepts for vector optimization problems. Among the problems that appear when the framework is generalized by considering set-valued functions, an increasing interest is generated by those involving monotone operators, especially now that new methods for approaching them by means of convex analysis have been developed. Following this path, the book provides several results on different properties of sums of monotone operators.
Author | : Radu Ioan Bot |
Publisher | : Springer Science & Business Media |
Total Pages | : 171 |
Release | : 2009-12-24 |
Genre | : Business & Economics |
ISBN | : 3642049001 |
Download Conjugate Duality in Convex Optimization Book in PDF, ePub and Kindle
The results presented in this book originate from the last decade research work of the author in the ?eld of duality theory in convex optimization. The reputation of duality in the optimization theory comes mainly from the major role that it plays in formulating necessary and suf?cient optimality conditions and, consequently, in generatingdifferent algorithmic approachesfor solving mathematical programming problems. The investigations made in this work prove the importance of the duality theory beyond these aspects and emphasize its strong connections with different topics in convex analysis, nonlinear analysis, functional analysis and in the theory of monotone operators. The ?rst part of the book brings to the attention of the reader the perturbation approach as a fundamental tool for developing the so-called conjugate duality t- ory. The classical Lagrange and Fenchel duality approaches are particular instances of this general concept. More than that, the generalized interior point regularity conditions stated in the past for the two mentioned situations turn out to be p- ticularizations of the ones given in this general setting. In our investigations, the perturbationapproachrepresentsthestartingpointforderivingnewdualityconcepts for several classes of convex optimization problems. Moreover, via this approach, generalized Moreau–Rockafellar formulae are provided and, in connection with them, a new class of regularity conditions, called closedness-type conditions, for both stable strong duality and strong duality is introduced. By stable strong duality we understand the situation in which strong duality still holds whenever perturbing the objective function of the primal problem with a linear continuous functional.
Author | : Radu Ioan Bot |
Publisher | : Springer Science & Business Media |
Total Pages | : 408 |
Release | : 2009-08-12 |
Genre | : Mathematics |
ISBN | : 3642028861 |
Download Duality in Vector Optimization Book in PDF, ePub and Kindle
This book presents fundamentals and comprehensive results regarding duality for scalar, vector and set-valued optimization problems in a general setting. One chapter is exclusively consecrated to the scalar and vector Wolfe and Mond-Weir duality schemes.
Author | : R. Tyrrell Rockafellar |
Publisher | : SIAM |
Total Pages | : 82 |
Release | : 1974-01-01 |
Genre | : Technology & Engineering |
ISBN | : 0898710138 |
Download Conjugate Duality and Optimization Book in PDF, ePub and Kindle
The theory of duality in problems of optimization is developed in a setting of finite and infinite dimensional spaces using convex analysis. Applications to convex and nonconvex problems. Expository account containing many new results. (Author).
Author | : Sorin-Mihai Grad |
Publisher | : |
Total Pages | : 217 |
Release | : 2014 |
Genre | : |
ISBN | : |
Download Recent Advances in Vector Optimization and Set-valued Analysis Via Convex Duality Book in PDF, ePub and Kindle
Author | : Ivan Singer |
Publisher | : Springer Science & Business Media |
Total Pages | : 366 |
Release | : 2007-03-12 |
Genre | : Mathematics |
ISBN | : 0387283951 |
Download Duality for Nonconvex Approximation and Optimization Book in PDF, ePub and Kindle
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.
Author | : Jonathan Borwein |
Publisher | : Springer Science & Business Media |
Total Pages | : 316 |
Release | : 2010-05-05 |
Genre | : Mathematics |
ISBN | : 0387312560 |
Download Convex Analysis and Nonlinear Optimization Book in PDF, ePub and Kindle
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.
Author | : Heinz H. Bauschke |
Publisher | : Springer |
Total Pages | : 624 |
Release | : 2017-02-28 |
Genre | : Mathematics |
ISBN | : 3319483110 |
Download Convex Analysis and Monotone Operator Theory in Hilbert Spaces Book in PDF, ePub and Kindle
This reference text, now in its second edition, offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis, monotone operator theory, and the fixed point theory of nonexpansive operators. Taking a unique comprehensive approach, the theory is developed from the ground up, with the rich connections and interactions between the areas as the central focus, and it is illustrated by a large number of examples. The Hilbert space setting of the material offers a wide range of applications while avoiding the technical difficulties of general Banach spaces. The authors have also drawn upon recent advances and modern tools to simplify the proofs of key results making the book more accessible to a broader range of scholars and users. Combining a strong emphasis on applications with exceptionally lucid writing and an abundance of exercises, this text is of great value to a large audience including pure and applied mathematicians as well as researchers in engineering, data science, machine learning, physics, decision sciences, economics, and inverse problems. The second edition of Convex Analysis and Monotone Operator Theory in Hilbert Spaces greatly expands on the first edition, containing over 140 pages of new material, over 270 new results, and more than 100 new exercises. It features a new chapter on proximity operators including two sections on proximity operators of matrix functions, in addition to several new sections distributed throughout the original chapters. Many existing results have been improved, and the list of references has been updated. Heinz H. Bauschke is a Full Professor of Mathematics at the Kelowna campus of the University of British Columbia, Canada. Patrick L. Combettes, IEEE Fellow, was on the faculty of the City University of New York and of Université Pierre et Marie Curie – Paris 6 before joining North Carolina State University as a Distinguished Professor of Mathematics in 2016.
Author | : Sorin-Mihai Grad |
Publisher | : |
Total Pages | : 18 |
Release | : 2012 |
Genre | : |
ISBN | : |
Download Vector Duality for Convex Vector Optimization Problems with Vector Respect to Quasi-minimality Book in PDF, ePub and Kindle
Author | : Mark Raymond Coodey |
Publisher | : |
Total Pages | : 126 |
Release | : 1997 |
Genre | : |
ISBN | : |
Download Examining Maximal Monotone Operators Using Pictures and Convex Functions Book in PDF, ePub and Kindle