A Duality Approach To Gap Functions For Variational Inequalities And Equilibrium Problems
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A Duality Approach To Gap Functions For Variational Inequalities And Equilibrium Problems
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Author : Altangerel Lkhamsuren
language : en
Publisher:
Release Date : 2006
A Duality Approach To Gap Functions For Variational Inequalities And Equilibrium Problems written by Altangerel Lkhamsuren and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
A Duality Approach To Gap Functions For Variational Inequalities And Equilibrium Problems
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Author :
language : en
Publisher:
Release Date : 2006
A Duality Approach To Gap Functions For Variational Inequalities And Equilibrium Problems written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
This work aims to investigate some applications of the conjugate duality for scalar and vector optimization problems to the construction of gap functions for variational inequalities and equilibrium problems. The basic idea of the approach is to reformulate variational inequalities and equilibrium problems into optimization problems depending on a fixed variable, which allows us to apply duality results from optimization problems. Based on some perturbations, first we consider the conjugate duality for scalar optimization. As applications, duality investigations for the convex partially separable optimization problem are discussed. Afterwards, we concentrate our attention on some applications of conjugate duality for convex optimization problems in finite and infinite-dimensional spaces to the construction of a gap function for variational inequalities and equilibrium problems. To verify the properties in the definition of a gap function weak and strong duality are used. The remainder of this thesis deals with the extension of this approach to vector variational inequalities and vector equilibrium problems. By using the perturbation functions in analogy to the scalar case, different dual problems for vector optimization and duality assertions for these problems are derived. This study allows us to propose some set-valued gap functions for the vector variational inequality. Finally, by applying the Fenchel duality on the basis of weak orderings, some variational principles for vector equilibrium problems are investigated.
Variational Inequalities And Network Equilibrium Problems
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Author : F. Giannessi
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Variational Inequalities And Network Equilibrium Problems written by F. Giannessi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Social Science categories.
This volume brings forth a set of papers presented at the conference on "Varia tional Inequalities and network equilibrium problems", held in Erice at the "G. Stam pacchia" School of the "E. Majorana" Centre for Scientific Culture in the period 19~25 June 1994. The meeting was conceived to contribute to the exchange between Variational Analysis and equilibrium problems, especially those related to network design. Most of the approaches and viewpoints of these fields are present in the volume, both as concerns the theory and the applications of equilibrium problems to transportation, computer and electric networks, to market behavior, and to bi~level programming. Being convinced of the great importance of equilibrium problems as well as of their complexity, the organizers hope that the merging of points of view coming from differ ent fields will stimulate theoretical research and applications. In this context Variational and Quasi~Variational Inequalities have shown them selves to be very important models for equilibrium problems. As a consequence in the last two decades they have received a lot of attention both as to mathematical inves tigation and applications. The proof that the above mentioned equilibrium problems can be expressed, in terms of Variational or Quasi~Variational Inequalities also in the non~standard and non~symmetric cases, has been a crucial improvement.
Duality In Optimization And Variational Inequalities
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Author : C.j. Goh
language : en
Publisher: Taylor & Francis
Release Date : 2002-05-10
Duality In Optimization And Variational Inequalities written by C.j. Goh and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-05-10 with Mathematics categories.
This comprehensive volume covers a wide range of duality topics ranging from simple ideas in network flows to complex issues in non-convex optimization and multicriteria problems. In addition, it examines duality in the context of variational inequalities and vector variational inequalities, as generalizations to optimization. Duality in Optimization and Variational Inequalities is intended for researchers and practitioners of optimization with the aim of enhancing their understanding of duality. It provides a wider appreciation of optimality conditions in various scenarios and under different assumptions. It will enable the reader to use duality to devise more effective computational methods, and to aid more meaningful interpretation of optimization and variational inequality problems.
On The Construction Of Gap Functions For Variational Inequalities Via Conjugate Duality
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Author : Altangerel Lkhamsuren
language : en
Publisher:
Release Date : 2005
On The Construction Of Gap Functions For Variational Inequalities Via Conjugate Duality written by Altangerel Lkhamsuren and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
Duality Principles In Nonconvex Systems
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Author : David Yang Gao
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Duality Principles In Nonconvex Systems written by David Yang Gao and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Motivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this book is the first to provide, within a unified framework, a self-contained comprehensive mathematical theory of duality for general non-convex, non-smooth systems, with emphasis on methods and applications in engineering mechanics. Topics covered include the classical (minimax) mono-duality of convex static equilibria, the beautiful bi-duality in dynamical systems, the interesting tri-duality in non-convex problems and the complicated multi-duality in general canonical systems. A potentially powerful sequential canonical dual transformation method for solving fully nonlinear problems is developed heuristically and illustrated by use of many interesting examples as well as extensive applications in a wide variety of nonlinear systems, including differential equations, variational problems and inequalities, constrained global optimization, multi-well phase transitions, non-smooth post-bifurcation, large deformation mechanics, structural limit analysis, differential geometry and non-convex dynamical systems. With exceptionally coherent and lucid exposition, the work fills a big gap between the mathematical and engineering sciences. It shows how to use formal language and duality methods to model natural phenomena, to construct intrinsic frameworks in different fields and to provide ideas, concepts and powerful methods for solving non-convex, non-smooth problems arising naturally in engineering and science. Much of the book contains material that is new, both in its manner of presentation and in its research development. A self-contained appendix provides some necessary background from elementary functional analysis. Audience: The book will be a valuable resource for students and researchers in applied mathematics, physics, mechanics and engineering. The whole volume or selected chapters can also be recommended as a text for both senior undergraduate and graduate courses in applied mathematics, mechanics, general engineering science and other areas in which the notions of optimization and variational methods are employed.
Canonical Duality Theory
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Author : David Yang Gao
language : en
Publisher: Springer
Release Date : 2017-10-09
Canonical Duality Theory written by David Yang Gao and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-09 with Mathematics categories.
This book on canonical duality theory provides a comprehensive review of its philosophical origin, physics foundation, and mathematical statements in both finite- and infinite-dimensional spaces. A ground-breaking methodological theory, canonical duality theory can be used for modeling complex systems within a unified framework and for solving a large class of challenging problems in multidisciplinary fields in engineering, mathematics, and the sciences. This volume places a particular emphasis on canonical duality theory’s role in bridging the gap between non-convex analysis/mechanics and global optimization. With 18 total chapters written by experts in their fields, this volume provides a nonconventional theory for unified understanding of the fundamental difficulties in large deformation mechanics, bifurcation/chaos in nonlinear science, and the NP-hard problems in global optimization. Additionally, readers will find a unified methodology and powerful algorithms for solving challenging problems in complex systems with real-world applications in non-convex analysis, non-monotone variational inequalities, integer programming, topology optimization, post-buckling of large deformed structures, etc. Researchers and graduate students will find explanation and potential applications in multidisciplinary fields.
Equilibrium Problems Nonsmooth Optimization And Variational Inequality Models
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Author : F. Giannessi
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-11
Equilibrium Problems Nonsmooth Optimization And Variational Inequality Models written by F. Giannessi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-11 with Mathematics categories.
The aim of the book is to cover the three fundamental aspects of research in equilibrium problems: the statement problem and its formulation using mainly variational methods, its theoretical solution by means of classical and new variational tools, the calculus of solutions and applications in concrete cases. The book shows how many equilibrium problems follow a general law (the so-called user equilibrium condition). Such law allows us to express the problem in terms of variational inequalities. Variational inequalities provide a powerful methodology, by which existence and calculation of the solution can be obtained.
Duality In Vector Optimization
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Author : Radu Ioan Bot
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-08-12
Duality In Vector Optimization written by Radu Ioan Bot and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-12 with Mathematics categories.
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.
A Posteriori Error Analysis Via Duality Theory
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Author : Weimin Han
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-11-19
A Posteriori Error Analysis Via Duality Theory written by Weimin Han and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-11-19 with Mathematics categories.
This work provides a posteriori error analysis for mathematical idealizations in modeling boundary value problems, especially those arising in mechanical applications, and for numerical approximations of numerous nonlinear var- tional problems. An error estimate is called a posteriori if the computed solution is used in assessing its accuracy. A posteriori error estimation is central to m- suring, controlling and minimizing errors in modeling and numerical appr- imations. In this book, the main mathematical tool for the developments of a posteriori error estimates is the duality theory of convex analysis, documented in the well-known book by Ekeland and Temam ([49]). The duality theory has been found useful in mathematical programming, mechanics, numerical analysis, etc. The book is divided into six chapters. The first chapter reviews some basic notions and results from functional analysis, boundary value problems, elliptic variational inequalities, and finite element approximations. The most relevant part of the duality theory and convex analysis is briefly reviewed in Chapter 2.