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Cover: 9783642542640 | Set-valued Optimization | An Introduction with Applications | Buch
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Set-valued Optimization
An Introduction with Applications
Buch von Akhtar A. Khan (u. a.)
Sprache: Englisch

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Beschreibung
Set-valued optimization is a vibrant and expanding branch of mathematics that deals with optimization problems where the objective map and/or the constraints maps are set-valued maps acting between certain spaces. Since set-valued maps subsumes single valued maps, set-valued optimization provides an important extension and unification of the scalar as well as the vector optimization problems. Therefore this relatively new discipline has justifiably attracted a great deal of attention in recent years. This book presents, in a unified framework, basic properties on ordering relations, solution concepts for set-valued optimization problems, a detailed description of convex set-valued maps, most recent developments in separation theorems, scalarization techniques, variational principles, tangent cones of first and higher order, sub-differential of set-valued maps, generalized derivatives of set-valued maps, sensitivity analysis, optimality conditions, duality and applications in economicsamong other things.
Set-valued optimization is a vibrant and expanding branch of mathematics that deals with optimization problems where the objective map and/or the constraints maps are set-valued maps acting between certain spaces. Since set-valued maps subsumes single valued maps, set-valued optimization provides an important extension and unification of the scalar as well as the vector optimization problems. Therefore this relatively new discipline has justifiably attracted a great deal of attention in recent years. This book presents, in a unified framework, basic properties on ordering relations, solution concepts for set-valued optimization problems, a detailed description of convex set-valued maps, most recent developments in separation theorems, scalarization techniques, variational principles, tangent cones of first and higher order, sub-differential of set-valued maps, generalized derivatives of set-valued maps, sensitivity analysis, optimality conditions, duality and applications in economicsamong other things.
Zusammenfassung

The first book on the growing subject of set-valued optimization

A highly simplified introduction to many complex issues in set-valued and vector optimization

Most up-to-date results which were so far only available in research papers

Includes supplementary material: [...]

Inhaltsverzeichnis
Introduction.- Order Relations and Ordering Cones.- Continuity and Differentiability.- Tangent Cones and Tangent Sets.- Nonconvex Separation Theorems.- Hahn-Banach Type Theorems.- Hahn-Banach Type Theorems.- Conjugates and Subdifferentials.- Duality.- Existence Results for Minimal Points.- Ekeland Variational Principle.- Derivatives and Epiderivatives of Set-valued Maps.- Optimality Conditions in Set-valued Optimization.- Sensitivity Analysis in Set-valued Optimization and Vector Variational Inequalities.- Numerical Methods for Solving Set-valued Optimization Problems.- Applications.
Details
Erscheinungsjahr: 2014
Fachbereich: Allgemeines
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Vector Optimization
Inhalt: xxii
765 S.
29 s/w Illustr.
765 p. 29 illus.
ISBN-13: 9783642542640
ISBN-10: 3642542646
Sprache: Englisch
Herstellernummer: 86108033
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Khan, Akhtar A.
Z¿linescu, Constantin
Tammer, Christiane
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Vector Optimization
Maße: 241 x 160 x 48 mm
Von/Mit: Akhtar A. Khan (u. a.)
Erscheinungsdatum: 28.10.2014
Gewicht: 1,332 kg
Artikel-ID: 105217699
Zusammenfassung

The first book on the growing subject of set-valued optimization

A highly simplified introduction to many complex issues in set-valued and vector optimization

Most up-to-date results which were so far only available in research papers

Includes supplementary material: [...]

Inhaltsverzeichnis
Introduction.- Order Relations and Ordering Cones.- Continuity and Differentiability.- Tangent Cones and Tangent Sets.- Nonconvex Separation Theorems.- Hahn-Banach Type Theorems.- Hahn-Banach Type Theorems.- Conjugates and Subdifferentials.- Duality.- Existence Results for Minimal Points.- Ekeland Variational Principle.- Derivatives and Epiderivatives of Set-valued Maps.- Optimality Conditions in Set-valued Optimization.- Sensitivity Analysis in Set-valued Optimization and Vector Variational Inequalities.- Numerical Methods for Solving Set-valued Optimization Problems.- Applications.
Details
Erscheinungsjahr: 2014
Fachbereich: Allgemeines
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Vector Optimization
Inhalt: xxii
765 S.
29 s/w Illustr.
765 p. 29 illus.
ISBN-13: 9783642542640
ISBN-10: 3642542646
Sprache: Englisch
Herstellernummer: 86108033
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Khan, Akhtar A.
Z¿linescu, Constantin
Tammer, Christiane
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Vector Optimization
Maße: 241 x 160 x 48 mm
Von/Mit: Akhtar A. Khan (u. a.)
Erscheinungsdatum: 28.10.2014
Gewicht: 1,332 kg
Artikel-ID: 105217699
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