Theory Of Vector Optimization

Author: Dinh The Luc
Editor: Springer
ISBN: 9783540505419
File Size: 29,41 MB
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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.
Theory of Vector Optimization
Language: en
Pages: 176
Authors: Dinh The Luc
Categories: Business & Economics
Type: BOOK - Published: 1988-12-07 - Publisher: Springer

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
Theory and Methods of Vector Optimization (Volume One)
Language: en
Pages: 195
Authors: Yu. K. Mashunin
Categories: Mathematics
Type: BOOK - Published: 2020-03-24 - Publisher: Cambridge Scholars Publishing

This first volume presents the theory and methods of solving vector optimization problems, using initial definitions that include axioms and the optimality principle. This book proves, mathematically, that the result it presents for the solution of the vector (multi-criteria) problem is the optimal outcome, and, as such, solves the problem
Encyclopedia of Optimization
Language: en
Pages: 4622
Authors: Christodoulos A. Floudas, Panos M. Pardalos
Categories: Mathematics
Type: BOOK - Published: 2008-09-04 - Publisher: Springer Science & Business Media

The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition
Vector Optimization with Infimum and Supremum
Language: en
Pages: 206
Authors: Andreas Löhne
Categories: Business & Economics
Type: BOOK - Published: 2011-05-25 - Publisher: Springer Science & Business Media

The theory of Vector Optimization is developed by a systematic usage of infimum and supremum. In order to get existence and appropriate properties of the infimum, the image space of the vector optimization problem is embedded into a larger space, which is a subset of the power set, in fact,
Optimality Conditions in Vector Optimization
Language: en
Pages: 184
Authors: Manuel Arana Jiménez, Gabriel Ruiz Garzón, Antonio Rufián Lizana
Categories: Mathematics
Type: BOOK - Published: 2010 - Publisher: Bentham Science Publishers

Vector optimization is continuously needed in several science fields, particularly in economy, business, engineering, physics and mathematics. The evolution of these fields depends, in part, on the improvements in vector optimization in mathematical programming. The aim of this Ebook is to present the latest developments in vector optimization. The contributions