LEADER 04867nam 22006255 450 001 9910861094803321 005 20240521125426.0 010 $a3-031-53476-X 024 7 $a10.1007/978-3-031-53476-8 035 $a(MiAaPQ)EBC31352140 035 $a(Au-PeEL)EBL31352140 035 $a(CKB)32139618300041 035 $a(DE-He213)978-3-031-53476-8 035 $a(EXLCZ)9932139618300041 100 $a20240521d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSecond-Order Variational Analysis in Optimization, Variational Stability, and Control $eTheory, Algorithms, Applications /$fby Boris S. Mordukhovich 205 $a1st ed. 2024. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2024. 215 $a1 online resource (802 pages) 225 1 $aSpringer Series in Operations Research and Financial Engineering,$x2197-1773 311 $a3-031-53475-1 320 $aIncludes bibliographical references and index. 327 $aPreface -- 1. Basic Concepts of Second-Order Analysis -- 2. Second-Order Subdifferential Calculus -- 3. Computing Second-Order Subdifferentials -- 4. Computing Primal-Dual Second-Order Objects -- 5. Tilt Stability in Optimization -- 6. Full Stability in Optimization -- 7. Full Stability for Parametric Variational Systems -- 8. Critical Multipliers in Variational Systems -- 9. Newton-Type Methods for Tilt-Stable Minimizers -- 10. Sweeping Process Over Controlled Polyhedra -- 11. Sweeping Process with Controlled Perturbations -- 12. Sweeping Process Under Prox-Regularity -- 13. Applications to Controlled Crowd Motion Models -- References -- List of Statements -- List of Figures -- Glossary of Notation -- Subject Index. 330 $aThis fundamental work is a sequel to monographs by the same author: Variational Analysis and Applications (2018) and the two Grundlehren volumes Variational Analysis and Generalized Differentiation: I Basic Theory, II Applications (2006). This present book is the first entirely devoted to second-order variational analysis with numerical algorithms and applications to practical models. It covers a wide range of topics including theoretical, numerical, and implementations that will interest researchers in analysis, applied mathematics, mathematical economics, engineering, and optimization. Inclusion of a variety of exercises and commentaries in each chapter allows the book to be used effectively in a course on this subject. This area has been well recognized as an important and rapidly developing area of nonlinear analysis and optimization with numerous applications. Consisting of 9 interrelated chapters, the book is self-contained with the inclusion of some preliminaries in Chapter 1. Results presented are useful tools for characterizations of fundamental notions of variational stability of solutions for diverse classes of problems in optimization and optimal control, the study of variational convexity of extended-real-valued functions and their specifications and variational sufficiency in optimization. Explicit calculations and important applications of second-order subdifferentials associated with the achieved characterizations of variational stability and related concepts, to the design and justification of second-order numerical algorithms for solving various classes of optimization problems, nonsmooth equations, and subgradient systems, are included. Generalized Newtonian algorithms are presented that show local and global convergence with linear, superlinear, and quadratic convergence rates. Algorithms are implemented to address interesting practical problems from the fields of machine learning, statistics, imaging, and other areas. 410 0$aSpringer Series in Operations Research and Financial Engineering,$x2197-1773 606 $aMathematical optimization 606 $aCalculus of variations 606 $aMathematical analysis 606 $aOperations research 606 $aManagement science 606 $aCalculus of Variations and Optimization 606 $aAnalysis 606 $aOperations Research, Management Science 615 0$aMathematical optimization. 615 0$aCalculus of variations. 615 0$aMathematical analysis. 615 0$aOperations research. 615 0$aManagement science. 615 14$aCalculus of Variations and Optimization. 615 24$aAnalysis. 615 24$aOperations Research, Management Science. 676 $a515.64 700 $aMordukhovich$b Boris S.$0499429 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910861094803321 996 $aSecond-Order Variational Analysis in Optimization, Variational Stability, and Control$94163444 997 $aUNINA