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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Authors and Affiliations

Institute of Mathematics, Hanoi, Vietnam

Dinh The Luc

Bibliographic Information

Book Title: Theory of Vector Optimization
Authors: Dinh The Luc
Series Title: Lecture Notes in Economics and Mathematical Systems
DOI: https://doi.org/10.1007/978-3-642-50280-4
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1989
Softcover ISBN: 978-3-540-50541-9Published: 07 December 1988
eBook ISBN: 978-3-642-50280-4Published: 06 December 2012
Series ISSN: 0075-8442
Series E-ISSN: 2196-9957
Edition Number: 1
Number of Pages: VIII, 176
Topics: Operations Research/Decision Theory

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Table of contents (6 chapters)

Front Matter

Analysis over Cones

Efficient Points and Vector Optimization Problems

Nonsmooth Vector Optimization Problems

Scalarization and Stability

Duality

Structure of Optimal Solution Sets

Back Matter

About this book