Vector Variational Inequalities and Vector Equilibria

Vector Variational Inequalities and Vector Equilibria
Title Vector Variational Inequalities and Vector Equilibria PDF eBook
Author F. Giannessi
Publisher Springer Science & Business Media
Pages 522
Release 2013-12-01
Genre Mathematics
ISBN 1461302994

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The book deals with the mathematical theory of vector variational inequalities with special reference to equilibrium problems. Such models have been introduced recently to study new problems from mechanics, structural engineering, networks, and industrial management, and to revisit old ones. The common feature of these problems is that given by the presence of concurrent objectives and by the difficulty of identifying a global functional (like energy) to be extremized. The vector variational inequalities have the advantage of both the variational ones and vector optimization which are found as special cases. Among several applications, the equilibrium flows on a network receive special attention. Audience: The book is addressed to academic researchers as well as industrial ones, in the fields of mathematics, engineering, mathematical programming, control theory, operations research, computer science, and economics.

Vector Variational Inequalities and Vector Optimization

Vector Variational Inequalities and Vector Optimization
Title Vector Variational Inequalities and Vector Optimization PDF eBook
Author Qamrul Hasan Ansari
Publisher Springer
Pages 517
Release 2017-10-31
Genre Business & Economics
ISBN 3319630490

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This book presents the mathematical theory of vector variational inequalities and their relations with vector optimization problems. It is the first-ever book to introduce well-posedness and sensitivity analysis for vector equilibrium problems. The first chapter provides basic notations and results from the areas of convex analysis, functional analysis, set-valued analysis and fixed-point theory for set-valued maps, as well as a brief introduction to variational inequalities and equilibrium problems. Chapter 2 presents an overview of analysis over cones, including continuity and convexity of vector-valued functions. The book then shifts its focus to solution concepts and classical methods in vector optimization. It describes the formulation of vector variational inequalities and their applications to vector optimization, followed by separate chapters on linear scalarization, nonsmooth and generalized vector variational inequalities. Lastly, the book introduces readers to vector equilibrium problems and generalized vector equilibrium problems. Written in an illustrative and reader-friendly way, the book offers a valuable resource for all researchers whose work involves optimization and vector optimization.

Vector Optimization

Vector Optimization
Title Vector Optimization PDF eBook
Author Guang-ya Chen
Publisher Springer Science & Business Media
Pages 324
Release 2005-07-13
Genre Business & Economics
ISBN 9783540212898

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This book is devoted to vector or multiple criteria approaches in optimization. Topics covered include: vector optimization, vector variational inequalities, vector variational principles, vector minmax inequalities and vector equilibrium problems. In particular, problems with variable ordering relations and set-valued mappings are treated. The nonlinear scalarization method is extensively used throughout the book to deal with various vector-related problems. The results presented are original and should be interesting to researchers and graduates in applied mathematics and operations research. Readers will benefit from new methods and ideas for handling multiple criteria decision problems.

Duality in Optimization and Variational Inequalities

Duality in Optimization and Variational Inequalities
Title Duality in Optimization and Variational Inequalities PDF eBook
Author C.j. Goh
Publisher CRC Press
Pages 330
Release 2002-05-10
Genre Mathematics
ISBN 1420018868

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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 Optimizati

Vector Optimization

Vector Optimization
Title Vector Optimization PDF eBook
Author Johannes Jahn
Publisher Springer Science & Business Media
Pages 471
Release 2013-06-05
Genre Business & Economics
ISBN 3540248285

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In vector optimization one investigates optimal elements such as min imal, strongly minimal, properly minimal or weakly minimal elements of a nonempty subset of a partially ordered linear space. The prob lem of determining at least one of these optimal elements, if they exist at all, is also called a vector optimization problem. Problems of this type can be found not only in mathematics but also in engineer ing and economics. Vector optimization problems arise, for exam ple, in functional analysis (the Hahn-Banach theorem, the lemma of Bishop-Phelps, Ekeland's variational principle), multiobjective pro gramming, multi-criteria decision making, statistics (Bayes solutions, theory of tests, minimal covariance matrices), approximation theory (location theory, simultaneous approximation, solution of boundary value problems) and cooperative game theory (cooperative n player differential games and, as a special case, optimal control problems). In the last decade vector optimization has been extended to problems with set-valued maps. This new field of research, called set optimiza tion, seems to have important applications to variational inequalities and optimization problems with multivalued data. The roots of vector optimization go back to F. Y. Edgeworth (1881) and V. Pareto (1896) who has already given the definition of the standard optimality concept in multiobjective optimization. But in mathematics this branch of optimization has started with the leg endary paper of H. W. Kuhn and A. W. Tucker (1951). Since about v Vl Preface the end of the 60's research is intensively made in vector optimization.

Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces

Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces
Title Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces PDF eBook
Author Michael Ulbrich
Publisher SIAM
Pages 315
Release 2011-07-28
Genre Mathematics
ISBN 1611970687

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A comprehensive treatment of semismooth Newton methods in function spaces: from their foundations to recent progress in the field. This book is appropriate for researchers and practitioners in PDE-constrained optimization, nonlinear optimization and numerical analysis, as well as engineers interested in the current theory and methods for solving variational inequalities.

Toward Interactive and Intelligent Decision Support Systems

Toward Interactive and Intelligent Decision Support Systems
Title Toward Interactive and Intelligent Decision Support Systems PDF eBook
Author Yoshikazu Sawaragi
Publisher
Pages 468
Release 1987
Genre Decision making
ISBN

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