04378nam 22006735 450 991029816990332120200706224318.03-319-63049-010.1007/978-3-319-63049-6(CKB)4100000001039303(DE-He213)978-3-319-63049-6(MiAaPQ)EBC5119464(PPN)222234024(EXLCZ)99410000000103930320171101d2018 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierVector Variational Inequalities and Vector Optimization Theory and Applications /by Qamrul Hasan Ansari, Elisabeth Köbis, Jen-Chih Yao1st ed. 2018.Cham :Springer International Publishing :Imprint: Springer,2018.1 online resource (XIII, 509 p. 60 illus., 1 illus. in color.) Vector Optimization,1867-89713-319-63048-2 Includes bibliographical references at the end of each chapters and index.Preliminaries -- Analysis over Cones -- Solution Concepts in Vector Optimization -- Classical Methods in Vector Optimization -- Vector Variational Inequalities -- Linear Scalarization of Vector Variational Inequalities -- Nonsmooth Vector Variational Inequalities -- Generalized Vector Variational Inequalities -- Vector Equilibrium Problems -- Generalized Vector Equilibrium Problems.This book presents the mathematical theory of vector variational inequalities and their relations with vector optimization problems. It is the first-ever book to introduce well-posedness and sensitivity analysis for vector equilibrium problems. The first chapter provides basic notations and results from the areas of convex analysis, functional analysis, set-valued analysis and fixed-point theory for set-valued maps, as well as a brief introduction to variational inequalities and equilibrium problems. Chapter 2 presents an overview of analysis over cones, including continuity and convexity of vector-valued functions. The book then shifts its focus to solution concepts and classical methods in vector optimization. It describes the formulation of vector variational inequalities and their applications to vector optimization, followed by separate chapters on linear scalarization, nonsmooth and generalized vector variational inequalities. Lastly, the book introduces readers to vector equilibrium problems and generalized vector equilibrium problems. Written in an illustrative and reader-friendly way, the book offers a valuable resource for all researchers whose work involves optimization and vector optimization.Vector Optimization,1867-8971Operations researchDecision makingMathematical optimizationCalculus of variationsManagement scienceOperations Research/Decision Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/521000Continuous Optimizationhttps://scigraph.springernature.com/ontologies/product-market-codes/M26030Calculus of Variations and Optimal Control; Optimizationhttps://scigraph.springernature.com/ontologies/product-market-codes/M26016Operations Research, Management Sciencehttps://scigraph.springernature.com/ontologies/product-market-codes/M26024Operations research.Decision making.Mathematical optimization.Calculus of variations.Management science.Operations Research/Decision Theory.Continuous Optimization.Calculus of Variations and Optimal Control; Optimization.Operations Research, Management Science.515.64Ansari Qamrul Hasanauthttp://id.loc.gov/vocabulary/relators/aut1060704Köbis Elisabethauthttp://id.loc.gov/vocabulary/relators/autYao Jen-Chihauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910298169903321Vector Variational Inequalities and Vector Optimization2514988UNINA