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Set-valued Optimization = An Introdu...
~
Zălinescu, Constantin.
Set-valued Optimization = An Introduction with Applications /
Record Type:
Language materials, printed : Monograph/item
Title/Author:
Set-valued Optimization/ by Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu.
Reminder of title:
An Introduction with Applications /
Author:
Khan, Akhtar A.
other author:
Tammer, Christiane.
Description:
XXII, 765 p. 29 illus.online resource. :
Contained By:
Springer Nature eBook
Subject:
Mathematical optimization. -
Online resource:
https://doi.org/10.1007/978-3-642-54265-7
ISBN:
9783642542657
Set-valued Optimization = An Introduction with Applications /
Khan, Akhtar A.
Set-valued Optimization
An Introduction with Applications /[electronic resource] :by Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu. - 1st ed. 2015. - XXII, 765 p. 29 illus.online resource. - Vector Optimization,1867-8971. - Vector Optimization,.
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.
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 economics among other things.
ISBN: 9783642542657
Standard No.: 10.1007/978-3-642-54265-7doiSubjects--Topical Terms:
527675
Mathematical optimization.
LC Class. No.: QA402.5-402.6
Dewey Class. No.: 519.6
Set-valued Optimization = An Introduction with Applications /
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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.
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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 economics among other things.
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