Theory of Vector Optimization: 319 (Lecture Notes in Economics and Mathematical Systems, 319) - Softcover

Theluc, Dinh

 
9783540505419: Theory of Vector Optimization: 319 (Lecture Notes in Economics and Mathematical Systems, 319)
Softcover
ISBN 10: 3540505415 ISBN 13: 9783540505419
Verlag: Springer, 1988

Inhaltsangabe

These notes grew out of a series of lectures given by the author at the Univer­ sity of Budapest during 1985-1986. Additional results have been included which were obtained while the author was at the University of Erlangen-Niirnberg under a grant of the Alexander von Humboldt Foundation. Vector optimization has two main sources coming from economic equilibrium and welfare theories of Edgeworth (1881) and Pareto (1906) and from mathemat­ ical backgrounds of ordered spaces of Cantor (1897) and Hausdorff (1906). Later, game theory of Borel (1921) and von Neumann (1926) and production theory of Koopmans (1951) have also contributed to this area. However, only in the fifties, after the publication of Kuhn-Tucker’s paper (1951) on the necessary and sufficient conditions for efficiency, and of Deubreu’s paper (1954) on valuation equilibrium and Pareto optimum, has vector optimization been recognized as a mathematical discipline. The stretching development of this field began later in the seventies and eighties. Today there are a number of books on vector optimization. Most of them are concerned with the methodology and the applications. Few of them offer a systematic study of the theoretical aspects. The aim of these notes is to pro­ vide a unified background of vector optimization,with the emphasis on nonconvex problems in infinite dimensional spaces ordered by convex cones. The notes are arranged into six chapters. The first chapter presents prelim­ inary material.

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Reseña del editor

These notes grew out of a series of lectures given by the author at the Univer­ sity of Budapest during 1985-1986. Additional results have been included which were obtained while the author was at the University of Erlangen-Niirnberg under a grant of the Alexander von Humboldt Foundation. Vector optimization has two main sources coming from economic equilibrium and welfare theories of Edgeworth (1881) and Pareto (1906) and from mathemat­ ical backgrounds of ordered spaces of Cantor (1897) and Hausdorff (1906). Later, game theory of Borel (1921) and von Neumann (1926) and production theory of Koopmans (1951) have also contributed to this area. However, only in the fifties, after the publication of Kuhn-Tucker's paper (1951) on the necessary and sufficient conditions for efficiency, and of Deubreu's paper (1954) on valuation equilibrium and Pareto optimum, has vector optimization been recognized as a mathematical discipline. The stretching development of this field began later in the seventies and eighties. Today there are a number of books on vector optimization. Most of them are concerned with the methodology and the applications. Few of them offer a systematic study of the theoretical aspects. The aim of these notes is to pro­ vide a unified background of vector optimization,with the emphasis on nonconvex problems in infinite dimensional spaces ordered by convex cones. The notes are arranged into six chapters. The first chapter presents prelim­ inary material.

Reseña del editor

This book presents a systematic study of the most important topics of vector optimization such as the existence of efficient points, optimality conditions, scalarization, duality, and the structure of optimal solutions sets. New methods to which particular attention is paid are the theory of nonconvex analysis or analysis over cones, the theory of contingent derivatives of set-valued maps, and the nonstandard approach to duality. By reading this book, graduate students can easily comprehend basic concepts and the most important methods of vector optimization. The researchers who are familiar with this theory will find in the book several new approaches to the subject together with the latest results on it.

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Verlag
Springer
Erscheinungsdatum
1988
Sprache
Englisch
ISBN 10 
3540505415
ISBN 13 
9783540505419
Einband
Tapa blanda
Anzahl der Seiten
188
Kontakt zum Hersteller
Nicht verfügbar
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