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Set-valued optimizationan introducti...

Khan, Akhtar A.

Set-valued optimizationan introduction with applications /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Set-valued optimizationby Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu.
其他題名:	an introduction with applications /
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)
電子資源:	http://dx.doi.org/10.1007/978-3-642-54265-7
ISBN:	9783642542657 (electronic bk.)

Set-valued optimizationan 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:

243402
Duality theory (Mathematics)

LC Class. No.: QA1

Dewey Class. No.: 519.3

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