LEADER 04220nam 22007695 450 001 9910447260103321 005 20251113194143.0 010 $a3-030-44723-5 024 7 $a10.1007/978-3-030-44723-6 035 $a(CKB)4100000011321170 035 $a(MiAaPQ)EBC6511720 035 $a(Au-PeEL)EBL6511720 035 $a(OCoLC)1162846016 035 $a(PPN)248596055 035 $a(MiAaPQ)EBC6240749 035 $a(MiAaPQ)EBC6240793 035 $a(MiAaPQ)EBC29090607 035 $a(DE-He213)978-3-030-44723-6 035 $a(EXLCZ)994100000011321170 100 $a20200628d2020 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aScalarization and Separation by Translation Invariant Functions $ewith Applications in Optimization, Nonlinear Functional Analysis, and Mathematical Economics /$fby Christiane Tammer, Petra Weidner 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (703 pages) $cillustrations 225 1 $aVector Optimization,$x1867-898X 311 08$a3-030-44721-9 327 $aIntroduction -- Sets and Binary Relations -- Extended Real-Valued Functions -- Translation Invariant Functions -- Minimizers of Translation Invariant Functions -- Vector Optimization in General Spaces -- Multiobjective Optimization -- Variational Analysis -- Special Cases and Functionals Related to ?A,k -- Set-Valued Optimization Problems -- Vector Optimization With Variable Domination Structures -- Variational Methods in Topological Vector Spaces -- Algorithms for the Solution of Optimization Problems -- Optimization Under Uncertainty -- Further Applications. . 330 $aLike norms, translation invariant functions are a natural and powerful tool for the separation of sets and scalarization. This book provides an extensive foundation for their application. It presents in a unified way new results as well as results which are scattered throughout the literature. The functions are defined on linear spaces and can be applied to nonconvex problems. Fundamental theorems for the function class are proved, with implications for arbitrary extended real-valued functions. The scope of applications is illustrated by chapters related to vector optimization, set-valued optimization, and optimization under uncertainty, by fundamental statements in nonlinear functional analysis and by examples from mathematical finance as well as from consumer and production theory. The book is written for students and researchers in mathematics and mathematical economics. Engineers and researchers from other disciplines can benefit from the applications, for example from scalarization methods for multiobjective optimization and optimal control problems. 410 0$aVector Optimization,$x1867-898X 606 $aOperations research 606 $aMathematical optimization 606 $aEconometrics 606 $aCalculus of variations 606 $aSocial sciences$xMathematics 606 $aOperations Research and Decision Theory 606 $aOptimization 606 $aQuantitative Economics 606 $aCalculus of Variations and Optimization 606 $aContinuous Optimization 606 $aMathematics in Business, Economics and Finance 615 0$aOperations research. 615 0$aMathematical optimization. 615 0$aEconometrics. 615 0$aCalculus of variations. 615 0$aSocial sciences$xMathematics. 615 14$aOperations Research and Decision Theory. 615 24$aOptimization. 615 24$aQuantitative Economics. 615 24$aCalculus of Variations and Optimization. 615 24$aContinuous Optimization. 615 24$aMathematics in Business, Economics and Finance. 676 $a515.63 676 $a515.63 700 $aTammer$b Christiane$0738596 702 $aWeidner$b Petra 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910447260103321 996 $aScalarization and separation by translation invariant functions$91901520 997 $aUNINA