LEADER 04933nam 22007455 450 001 9910254284403321 005 20200704053244.0 010 $a9783319642772$belectronic book 010 $a3319642774$belectronic book 010 $z9783319642765$bprint 010 $z3319642766$bprint 024 7 $a10.1007/978-3-319-64277-2 035 $a(CKB)4100000000881630 035 $a(DE-He213)978-3-319-64277-2 035 $a(MiAaPQ)EBC5115914 035 $a(PPN)220125090 035 $a(EXLCZ)994100000000881630 100 $a20171028d2017 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aVariational Analysis of Regular Mappings $eTheory and Applications /$fby Alexander D. Ioffe 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XXI, 495 p. 11 illus., 2 illus. in color.) 225 1 $aSpringer Monographs in Mathematics,$x1439-7382 320 $aIncludes bibliographical references and index. 327 $a1 The Classical Theory -- 2 Metric Theory: Phenomenology -- 3 Metric Theory: The Infinitesimal Viewpoint -- 4 Subdifferentials: A Short Introduction -- 5 Banach Space Theory: Regularity Criteria -- 6 Banach Space Theory: Special Classes of Mappings -- 7 Applications to Analysis and Optimization 1 -- 8 Regularity in Finite-Dimensional Spaces -- 9 Applications to Analysis and Optimization 2. 330 $aThis monograph offers the first systematic account of (metric) regularity theory in variational analysis. It presents new developments alongside classical results and demonstrates the power of the theory through applications to various problems in analysis and optimization theory. The origins of metric regularity theory can be traced back to a series of fundamental ideas and results of nonlinear functional analysis and global analysis centered around problems of existence and stability of solutions of nonlinear equations. In variational analysis, regularity theory goes far beyond the classical setting and is also concerned with non-differentiable and multi-valued operators. The present volume explores all basic aspects of the theory, from the most general problems for mappings between metric spaces to those connected with fairly concrete and important classes of operators acting in Banach and finite dimensional spaces. Written by a leading expert in the field, the book covers new and powerful techniques, which have proven to be highly efficient even in classical settings, and outlines the theory?s predominantly quantitative character, leading to a variety of new and unexpected applications. Variational Analysis of Regular Mappings is aimed at graduate students and researchers in nonlinear and functional analysis, especially those working in areas close to optimization and optimal control, and will be suitable to anyone interested in applying new concepts and ideas to operations research, control engineering and numerical analysis. 410 0$aSpringer Monographs in Mathematics,$x1439-7382 606 $aCalculus of variations 606 $aMathematical optimization 606 $aFunctional analysis 606 $aGlobal analysis (Mathematics) 606 $aManifolds (Mathematics) 606 $aDifference equations 606 $aFunctional equations 606 $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016 606 $aContinuous Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26030 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aGlobal Analysis and Analysis on Manifolds$3https://scigraph.springernature.com/ontologies/product-market-codes/M12082 606 $aDifference and Functional Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12031 615 0$aCalculus of variations. 615 0$aMathematical optimization. 615 0$aFunctional analysis. 615 0$aGlobal analysis (Mathematics). 615 0$aManifolds (Mathematics). 615 0$aDifference equations. 615 0$aFunctional equations. 615 14$aCalculus of Variations and Optimal Control; Optimization. 615 24$aContinuous Optimization. 615 24$aFunctional Analysis. 615 24$aGlobal Analysis and Analysis on Manifolds. 615 24$aDifference and Functional Equations. 676 $a515.64 700 $aIoffe$b Alexander D$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767473 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254284403321 996 $aVariational Analysis of Regular Mappings$91562481 997 $aUNINA