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Set-valued optimization[electronic resource] :an introduction with applications /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	519.3
書名/作者:	Set-valued optimization : an introduction with applications // by Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu.
作者:	Khan, Akhtar A.
其他作者:	Tammer, Christiane.
出版者:	Berlin, Heidelberg : : Springer Berlin Heidelberg :, 2015.
面頁冊數:	xxii, 765 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Duality theory (Mathematics)
標題:	Mathematical optimization.
標題:	Set-valued maps.
標題:	Programming (Mathematics)
標題:	Mathematics.
標題:	Optimization.
標題:	Operation Research/Decision Theory.
標題:	Continuous Optimization.
標題:	Operations Research, Management Science.
標題:	Game Theory, Economics, Social and Behav. Sciences.
ISBN:	9783642542657 (electronic bk.)
ISBN:	9783642542640 (paper)
內容註:	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.
摘要、提要註:	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.
電子資源:	http://dx.doi.org/10.1007/978-3-642-54265-7

Set-valued optimization[electronic resource] :an introduction with applications /
Khan, Akhtar A.

Set-valued optimizationan introduction with applications /[electronic resource] :by Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu. - Berlin, Heidelberg :Springer Berlin Heidelberg :2015. - xxii, 765 p. :ill., digital ;24 cm. - 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 (electronic bk.)

Standard No.: 10.1007/978-3-642-54265-7doiSubjects--Topical Terms:

511759
Duality theory (Mathematics)

LC Class. No.: QA1

Dewey Class. No.: 519.3

Set-valued optimization[electronic resource] :an introduction with applications /
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