04237nam a22005415i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118040002500153050001400178050001200192050002000204072001700224072002300241072001600264072001500280082001500295100008100310245012100391264007500512300006400587336002600651337002600677338003600703347002400739490005100763505039700814520156301211650003102774650002502805650002102830650002602851650013302877650010003010650009603110650011803206650011203324710003403436773002003470776003603490776003603526776003603562830005103598856004603649978-3-319-64277-2DE-He21320181204134425.0cr nn 008mamaa171028s2017 gw | s |||| 0|eng d a97833196427727 a10.1007/978-3-319-64277-22doi aISI Library, Kolkata 4aQA315-316 4aQA402.3 4aQA402.5-QA402.6 7aPBKQ2bicssc 7aMAT0050002bisacsh 7aPBKQ2thema 7aPBU2thema04a515.642231 aIoffe, Alexander D.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aVariational Analysis of Regular Mappingsh[electronic resource] :bTheory and Applications /cby Alexander D. Ioffe. 1aCham :bSpringer International Publishing :bImprint: Springer,c2017. aXXI, 495 p. 11 illus., 2 illus. in color.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aSpringer Monographs in Mathematics,x1439-73820 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. 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. 0aMathematical optimization. 0aFunctional analysis. 0aGlobal analysis. 0aFunctional equations.14aCalculus of Variations and Optimal Control; Optimization.0http://scigraph.springernature.com/things/product-market-codes/M2601624aContinuous Optimization.0http://scigraph.springernature.com/things/product-market-codes/M2603024aFunctional Analysis.0http://scigraph.springernature.com/things/product-market-codes/M1206624aGlobal Analysis and Analysis on Manifolds.0http://scigraph.springernature.com/things/product-market-codes/M1208224aDifference and Functional Equations.0http://scigraph.springernature.com/things/product-market-codes/M120312 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z978331964276508iPrinted edition:z978331964278908iPrinted edition:z9783319877617 0aSpringer Monographs in Mathematics,x1439-738240uhttps://doi.org/10.1007/978-3-319-64277-2