LEADER 03669nam 22005775 450 001 9910564678903321 005 20251113201437.0 010 $a9783030947859 010 $a3030947858 024 7 $a10.1007/978-3-030-94785-9 035 $a(MiAaPQ)EBC6962087 035 $a(Au-PeEL)EBL6962087 035 $a(CKB)21605624700041 035 $a(PPN)262167972 035 $a(OCoLC)1313909071 035 $a(DE-He213)978-3-030-94785-9 035 $a(EXLCZ)9921605624700041 100 $a20220424d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aConvex Analysis and Beyond $eVolume I: Basic Theory /$fby Boris S. Mordukhovich, Nguyen Mau Nam 205 $a1st ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2022. 215 $a1 online resource (597 pages) 225 1 $aSpringer Series in Operations Research and Financial Engineering,$x2197-1773 311 08$aPrint version: Mordukhovich, Boris S. Convex Analysis and Beyond Cham : Springer International Publishing AG,c2022 9783030947842 327 $aFundamentals -- Basic theory of convexity -- Convex generalized differentiation -- Enhanced calculus and fenchel duality -- Variational techniques and further subgradient study -- Miscellaneous topics on convexity -- Convexified Lipschitzian analysis -- List of Figures -- Glossary of Notation and Acronyms -- Subject Index. 330 $aThis book presents a unified theory of convex functions, sets, and set-valued mappings in topological vector spaces with its specifications to locally convex, Banach and finite-dimensional settings. These developments and expositions are based on the powerful geometric approach of variational analysis, which resides on set extremality with its characterizations and specifications in the presence of convexity. Using this approach, the text consolidates the device of fundamental facts of generalized differential calculus to obtain novel results for convex sets, functions, and set-valued mappings in finite and infinite dimensions. It also explores topics beyond convexity using the fundamental machinery of convex analysis to develop nonconvex generalized differentiation and its applications. The text utilizes an adaptable framework designed with researchers as well as multiple levels of students in mind. It includes many exercises and figures suited to graduate classesin mathematical sciences that are also accessible to advanced students in economics, engineering, and other applications. In addition, it includes chapters on convex analysis and optimization in finite-dimensional spaces that will be useful to upper undergraduate students, whereas the work as a whole provides an ample resource to mathematicians and applied scientists, particularly experts in convex and variational analysis, optimization, and their applications. . 410 0$aSpringer Series in Operations Research and Financial Engineering,$x2197-1773 606 $aMathematical optimization 606 $aNumerical analysis 606 $aOptimization 606 $aNumerical Analysis 615 0$aMathematical optimization. 615 0$aNumerical analysis. 615 14$aOptimization. 615 24$aNumerical Analysis. 676 $a516.08 676 $a515.882 700 $aMordukhovich$b B. Sh$g(Boris Sholimovich),$0499429 702 $aNguyen$b Mau Nam 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910564678903321 996 $aConvex analysis and beyond$92965901 997 $aUNINA