LEADER 04526nam 22005535 450 001 9910770264403321 005 20231208002809.0 010 $a3-031-36534-8 024 7 $a10.1007/978-3-031-36534-8 035 $a(CKB)29310824700041 035 $a(DE-He213)978-3-031-36534-8 035 $a(MiAaPQ)EBC31005755 035 $a(Au-PeEL)EBL31005755 035 $a(MiAaPQ)EBC31132531 035 $a(Au-PeEL)EBL31132531 035 $a(EXLCZ)9929310824700041 100 $a20231208d2023 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aVariational Methods in Partially Ordered Spaces$b[electronic resource] /$fby Alfred Göpfert, Hassan Riahi, Christiane Tammer, Constantin Z?linescu 205 $a2nd ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2023. 215 $a1 online resource (XXVIII, 553 p. 26 illus., 23 illus. in color.) 225 1 $aCMS/CAIMS Books in Mathematics,$x2730-6518 ;$v7 311 08$a9783031365331 327 $aExamples -- Functional Analysis over Cones -- Optimization in Partially Ordered Spaces -- Applications. 330 $aIn mathematical modeling of processes occurring in logistics, management science, operations research, networks, mathematical finance, medicine, and control theory, one often encounters optimization problems involving more than one objective function so that Multiobjective Optimization (or Vector Optimization, initiated by W. Pareto) has received new impetus. The growing interest in vector optimization problems, both from the theoretical point of view and as it concerns applications to real world optimization problems, asks for a general scheme which embraces several existing developments and stimulates new ones. This book aims to provide the newest results and applications of this quickly growing field. Basic tools of partially ordered spaces are discussed and applied to variational methods in nonlinear analysis and to optimization problems. The book begins by providing simple examples that illustrate what kind of problems can be handled with the methods presented. The book then deals with connections between order structures and topological structures of sets, discusses properties of nonlinear scalarization functions, and derives corresponding separation theorems for not necessarily convex sets. Furthermore, characterizations of set relations via scalarization are presented. Important topological properties of multifunctions and new results concerning the theory of vector optimization and equilibrium problems are presented in the book. These results are applied to construct numerical algorithms, especially, proximal-point algorithms and geometric algorithms based on duality assertions. In the second edition, new sections about set less relations, optimality conditions in set optimization and the asymptotic behavior of multiobjective Pareto-equilibrium problems have been incorporated. Furthermore, a new chapter regarding scalar optimization problems under uncertainty and robust counterpart problems employing approaches based on vector optimization, set optimization, and nonlinear scalarization was added. Throughout the entire book, there are examples used to illustrate the results and check the stated conditions. This book will be of interest to graduate students and researchers in pure and applied mathematics, economics, and engineering. A sound knowledge of linear algebra and introductory real analysis should provide readers with sufficient background for this book. . 410 0$aCMS/CAIMS Books in Mathematics,$x2730-6518 ;$v7 606 $aOperations research 606 $aManagement science 606 $aOperations Research, Management Science 615 0$aOperations research. 615 0$aManagement science. 615 14$aOperations Research, Management Science . 676 $a003 700 $aGöpfert$b Alfred$4aut$4http://id.loc.gov/vocabulary/relators/aut$057904 702 $aRiahi$b Hassan$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aTammer$b Christiane$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aZ?linescu$b Constantin$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910770264403321 996 $aVariational Methods in Partially Ordered Spaces$93660371 997 $aUNINA