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Vector Optimization
Johannes Jahn (Gebundene Ausgabe, Englisch)
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Optischer Zustand
Beschreibung
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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
21.01.2004
Sprache
Englisch
EAN
9783540206156
Herausgeber
Springer Berlin
Sonderedition
Nein
Autor
Johannes Jahn
Seitenanzahl
465
Auflage
1
Einbandart
Gebundene Ausgabe
Buch Untertitel
Theory, Applications, and Extensions
Thema-Inhalt
KJT - Unternehmensforschung
KJMD - Management: Entscheidungstheorie
PBU - Optimierung
PBK - Mathematische Analysis, allgemein
KJT - Unternehmensforschung
KJM - Management und Managementtechniken
Inhaltsverzeichnis
Convex Analysis: Linear Spaces.- Maps on Linear Spaces.- Some Fundamental Theorems.- Theory of Vector Optimization: Optimality Notions.- Scalarization.- Existence Theorems.- Generalized Lagrange Multiplier Rule.- Duality.- Mathematical Applications: Vector Approximation.- Cooperative n Player Differential Games.- Engineering Applications: Theoretical Basics of Multiobjective Optimization.- Numerical Methods.- Multiobjective Design Problems.- Extensions to Set Optimization: Basic Concepts and Results of Set Optimization.- Contingent Epiderivatives.- Subdifferential.- Optimality Conditions.
Höhe
235 mm
Breite
15.5 cm
-.-
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