04704nam 22008055 450 991030026040332120200702154439.03-642-54265-410.1007/978-3-642-54265-7(CKB)3710000000262153(EBL)1968316(OCoLC)894915420(SSID)ssj0001372229(PQKBManifestationID)11802163(PQKBTitleCode)TC0001372229(PQKBWorkID)11302387(PQKB)10868873(DE-He213)978-3-642-54265-7(MiAaPQ)EBC1968316(PPN)258857935(PPN)182099997(EXLCZ)99371000000026215320141020d2015 u| 0engur|n|---|||||txtccrSet-valued Optimization An Introduction with Applications /by Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu1st ed. 2015.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2015.1 online resource (781 p.)Vector Optimization,1867-8971Description based upon print version of record.3-642-54264-6 Includes bibliographical references and index.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.Vector Optimization,1867-8971Mathematical optimizationOperations researchDecision makingManagement scienceGame theoryOptimizationhttps://scigraph.springernature.com/ontologies/product-market-codes/M26008Operations Research/Decision Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/521000Continuous Optimizationhttps://scigraph.springernature.com/ontologies/product-market-codes/M26030Operations Research, Management Sciencehttps://scigraph.springernature.com/ontologies/product-market-codes/M26024Game Theory, Economics, Social and Behav. Scienceshttps://scigraph.springernature.com/ontologies/product-market-codes/M13011Mathematical optimization.Operations research.Decision making.Management science.Game theory.Optimization.Operations Research/Decision Theory.Continuous Optimization.Operations Research, Management Science.Game Theory, Economics, Social and Behav. Sciences.510519519.6658.40301Khan Akhtar Aauthttp://id.loc.gov/vocabulary/relators/aut768286Tammer Christianeauthttp://id.loc.gov/vocabulary/relators/autZălinescu Constantinauthttp://id.loc.gov/vocabulary/relators/autBOOK9910300260403321Set-valued Optimization2521526UNINA