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020 _a9783031534768
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024 7 _a10.1007/978-3-031-53476-8
_2doi
050 4 _aQA402.5-402.6
050 4 _aQA315-316
072 7 _aPBU
_2bicssc
072 7 _aMAT042000
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072 7 _aPBU
_2thema
100 1 _aMordukhovich, Boris S.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_977130
245 1 0 _aSecond-Order Variational Analysis in Optimization, Variational Stability, and Control
_h[electronic resource] :
_bTheory, Algorithms, Applications /
_cby Boris S. Mordukhovich.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2024.
300 _aXVIII, 789 p. 24 illus., 21 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Series in Operations Research and Financial Engineering,
_x2197-1773
505 0 _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.
520 _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.
650 0 _aMathematical optimization.
_965522
650 0 _aCalculus of variations.
_967268
650 0 _aMathematical analysis.
_964178
650 0 _aOperations research.
_957943
650 0 _aManagement science.
_957941
650 1 4 _aCalculus of Variations and Optimization.
_967270
650 2 4 _aAnalysis.
650 2 4 _aOperations Research, Management Science.
_965527
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031534751
776 0 8 _iPrinted edition:
_z9783031534775
776 0 8 _iPrinted edition:
_z9783031534782
830 0 _aSpringer Series in Operations Research and Financial Engineering,
_x2197-1773
_976963
856 4 0 _uhttps://doi.org/10.1007/978-3-031-53476-8
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c59993
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