LEADER 04117nam 22006495 450 001 9910734837003321 005 20251113182408.0 010 $a3-031-29551-X 024 7 $a10.1007/978-3-031-29551-5 035 $a(CKB)27559748700041 035 $a(DE-He213)978-3-031-29551-5 035 $a(PPN)272250759 035 $a(MiAaPQ)EBC31093848 035 $a(Au-PeEL)EBL31093848 035 $a(EXLCZ)9927559748700041 100 $a20230711d2023 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFundamentals of Convex Analysis and Optimization $eA Supremum Function Approach /$fby Rafael Correa, Abderrahim Hantoute, Marco A. López 205 $a1st ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2023. 215 $a1 online resource (XIII, 444 p. 1 illus.) 225 1 $aSpringer Series in Operations Research and Financial Engineering,$x2197-1773 311 08$a9783031295508 320 $aIncludes bibliographical references and index. 327 $a1. Introduction -- 2. Preliminaries -- 3. Fenchel-Moreau-Rockafellar theory -- 4. Fundamental topics in convex analysis -- 5. Supremum of convex functions -- 6. The supremum in specific contexts -- 7. Other subdifferential calculus rules -- 8. Miscellaneous -- 9. Exercises - Solutions -- Index -- Glossary of Notations -- Bibliography. 330 $aThis book aims at an innovative approach within the framework of convex analysis and optimization, based on an in-depth study of the behavior and properties of the supremum of families of convex functions. It presents an original and systematic treatment of convex analysis, covering standard results and improved calculus rules in subdifferential analysis. The tools supplied in the text allow a direct approach to the mathematical foundations of convex optimization, in particular to optimality and duality theory. Other applications in the book concern convexification processes in optimization, non-convex integration of the Fenchel subdifferential, variational characterizations of convexity, and the study of Chebychev sets. At the same time, the underlying geometrical meaning of all the involved concepts and operations is highlighted and duly emphasized. A notable feature of the book is its unifying methodology, as well as the novelty of providing an alternative or complementary view to the traditional one in which the discipline is presented to students and researchers. This textbook can be used for courses on optimization, convex and variational analysis, addressed to graduate and post-graduate students of mathematics, and also students of economics and engineering. It is also oriented to provide specific background for courses on optimal control, data science, operations research, economics (game theory), etc. The book represents a challenging and motivating development for those experts in functional analysis, convex geometry, and any kind of researchers who may be interested in applications of their work. 410 0$aSpringer Series in Operations Research and Financial Engineering,$x2197-1773 606 $aOperations research 606 $aManagement science 606 $aMathematical optimization 606 $aFunctional analysis 606 $aOperations Research, Management Science 606 $aOptimization 606 $aFunctional Analysis 615 0$aOperations research. 615 0$aManagement science. 615 0$aMathematical optimization. 615 0$aFunctional analysis. 615 14$aOperations Research, Management Science. 615 24$aOptimization. 615 24$aFunctional Analysis. 676 $a515.882 676 $a515.882 700 $aCorrea$b Rafael$f1890-$01860082 702 $aHantoute$b Abderrahim 702 $aLo?pez$b Marco A. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910734837003321 996 $aFundamentals of Convex Analysis and Optimization$94464583 997 $aUNINA