# Download Vector Optimization: Theory, Applications, and Extensions eBook

## by **Johannes Jahn**

In vector optimization one investigates optimal elements such as min imal, strongly minimal, properly minimal or. .

The prob lem of determining at least one of these optimal elements, if they exist at all, is also called a vector optimization problem. 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. Tucker (1951).

Fundamentals and important results of vector optimization in a general setting are presented in this book. The theory developed includes scalarization, existence theorems, a generalized Lagrange multiplier rule and duality results

Fundamentals and important results of vector optimization in a general setting are presented in this book. The theory developed includes scalarization, existence theorems, a generalized Lagrange multiplier rule and duality results

This book presents fundamentals and important results of vector optimization in a general setting. Applications to vector approximation, cooperative game theory and multiobjective optimization are described.

This book presents fundamentals and important results of vector optimization in a general setting. The theory developed includes scalarization, existence theorems, a generalized Lagrange multiplier rule and duality results. The theory is extended to set optimization with particular emphasis on contingent epiderivatives, subgradients and optimality conditions. Background material of convex analysis being necessary is concisely summarized at the beginning.

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Mathematical Applications: Vector Approximation. Cooperative n Player Differential Games. oceedings{Jahn2004VectorO, title {Vector optimization - theory, applications, and extensions}, author {Johannes Jahn}, year {2004} }. Johannes Jahn. Engineering Applications: Theoretical Basics of Multiobjective Optimization. Multiobjective Design Problems. Extensions to Set Optimization: Basic Concepts and Results of Set Optimization. Contingent Epiderivatives. Optimality Conditions. Convex Analysis: Linear Spaces. Maps on Linear Spaces. Some Fundamental Theorems.

Jahn, well known by his papers and books on convex analysis and optimizatio. rote this interesting book that gives a clear insight into theory and application of vector optimization. It is not only a revised version of the book from 198. ut he also extended the contents considerabl.Alfred Göpfert, Zentralblatt MATH, Vol. 1055, 2005). This volume is a revised and substantially enlarged version of the author’s boo.

Автор: Jahn Johannes Название: Vector Optimization, Theory, Applications, and Extensions Издательство .

The theory is extended to set optimization with particular emphasis on contingent epiderivatives, subgradients and optimality conditions.

Items related to Vector Optimization: Theory, Applications, and Extensions. J. Jahn, well known by his papers and books on convex analysis and optimization a ] wrote this interesting book that gives a clear insight into theory and application of vector optimization. Jahn, Johannes Vector Optimization: Theory, Applications, and Extensions. ISBN 13: 9783642170041. Vector Optimization: Theory, Applications, and Extensions. It is not only a revised version of the book from 1986 a ] but he also extended the contents considerably a . (Alfred GApfert, Zentralblatt MATH, Vol.

Fundamentals and important results of vector optimization in a general setting are presented in this book. The theory developed includes scalarization, existence theorems, a generalized Lagrange multiplier rule and duality results. Applications to vector approximation, cooperative game theory and multiobjective optimization are described. The theory is extended to set optimization with particular emphasis on contingent epiderivatives, subgradients and optimality conditions. Background material of convex analysis being necessary is concisely summarized at the beginning.

This second edition contains new parts on the adaptive Eichfelder-Polak method, a concrete application to magnetic resonance systems in medical engineering and additional remarks on the contribution of F.Y. Edgeworth and V. Pareto. The bibliography is updated and includes more recent important publications.