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＜E-Book＞
Set-valued Optimization : An Introduction with Applications / by Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu
(Vector Optimization. ISSN:1867898X)

Edition	1st ed. 2015.
Publisher	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Year	2015
Language	English
Size	XXII, 765 p. 29 illus : online resource
Authors	*Khan, Akhtar A author Tammer, Christiane author Zălinescu, Constantin author SpringerLink (Online service)
Subjects	LCSH:Mathematical optimization LCSH:Operations research LCSH:Management science LCSH:Game theory FREE:Optimization FREE:Operations Research and Decision Theory FREE:Continuous Optimization FREE:Operations Research, Management Science FREE:Game Theory
Notes	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 economicsamong other things HTTP:URL=https://doi.org/10.1007/978-3-642-54265-7

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