Set-valued Optimization [electronic resource] : An Introduction with Applications / by Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu.
Contributor(s): Tammer, Christiane [author.] | Zălinescu, Constantin [author.] | SpringerLink (Online service)Material type: TextSeries: Vector Optimization: Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2015Description: XXII, 765 p. 29 illus. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783642542657Subject(s): Mathematics | Operations research | Decision making | Game theory | Mathematical optimization | Management science | Mathematics | Optimization | Operation Research/Decision Theory | Continuous Optimization | Operations Research, Management Science | Game Theory, Economics, Social and Behav. SciencesAdditional physical formats: Printed edition:: No titleDDC classification: 519.6 LOC classification: QA402.5-402.6Online resources: Click here to access online
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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.
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.