LEADER 05296nam 22007455 450 001 9910299990603321 005 20200703081852.0 010 $a1-4939-1037-X 024 7 $a10.1007/978-1-4939-1037-3 035 $a(CKB)3710000000143784 035 $a(EBL)1782062 035 $a(SSID)ssj0001276093 035 $a(PQKBManifestationID)11726779 035 $a(PQKBTitleCode)TC0001276093 035 $a(PQKBWorkID)11239134 035 $a(PQKB)11447574 035 $a(DE-He213)978-1-4939-1037-3 035 $a(MiAaPQ)EBC6312675 035 $a(MiAaPQ)EBC1782062 035 $a(Au-PeEL)EBL1782062 035 $a(CaPaEBR)ebr10976175 035 $a(OCoLC)881688772 035 $a(PPN)179767305 035 $a(EXLCZ)993710000000143784 100 $a20140618d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aImplicit Functions and Solution Mappings $eA View from Variational Analysis /$fby Asen L. Dontchev, R. Tyrrell Rockafellar 205 $a2nd ed. 2014. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2014. 215 $a1 online resource (495 p.) 225 1 $aSpringer Series in Operations Research and Financial Engineering,$x1431-8598 300 $aDescription based upon print version of record. 311 $a1-4939-1036-1 320 $aIncludes bibliographical references and index. 327 $aIntroduction and equation-solving background -- Solution mappings for variational problems -- Set-valued analysis of solution mappings -- Regularity properties through generalized derivatives -- Metric regularity in infinite dimensions -- Applications in numerical variational analysis. 330 $aThe implicit function theorem is one of the most important theorems in analysis and its many variants are basic tools in partial differential equations and numerical analysis. This second edition of Implicit Functions and Solution Mappings presents an updated and more complete picture of the field by including solutions of problems that have been solved since the first edition was published, and places old and new results in a broader perspective. The purpose of this self-contained work is to provide a reference on the topic and to provide a unified collection of a number of results which are currently scattered throughout the literature. Updates to this edition include new sections in almost all chapters, new exercises and examples, updated commentaries to chapters and an enlarged index and references section. From reviews of the first edition: ?The book commences with a helpful context-setting preface followed by six chapters. Each chapter starts with a useful preamble and concludes with a careful and instructive commentary, while a good set of references, a notation guide, and a somewhat brief index complete this study. ? I unreservedly recommended this book to all practitioners and graduate students interested in modern optimization theory or control theory or to those just engaged by beautiful analysis cleanly described.? (Jonathan Michael Borwein, IEEE Control Systems Magazine, February, 2012) ?This book is devoted to the theory of inverse and implicit functions and some of its modifications for solution mappings in variational problems. ? The book is targeted to a broad audience of researchers, teachers and graduate students. It can be used as well as a textbook as a reference book on the topic. Undoubtedly, it will be used by mathematicians dealing with functional and numerical analysis, optimization, adjacent branches and also by specialists in mechanics, physics, engineering, economics, and so on.? (Peter Zabreiko, Zentralblatt MATH, Vol. 1178, 2010) ?The present monograph will be a most welcome and valuable addition. ? This book will save much time and effort, both for those doing research in variational analysis and for students learning the field. This important contribution fills a gap in the existing literature.? (Stephen M. Robinson, Mathematical Reviews, Issue 2010). 410 0$aSpringer Series in Operations Research and Financial Engineering,$x1431-8598 606 $aMathematical optimization 606 $aMathematical analysis 606 $aAnalysis (Mathematics) 606 $aNumerical analysis 606 $aOptimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26008 606 $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007 606 $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050 615 0$aMathematical optimization. 615 0$aMathematical analysis. 615 0$aAnalysis (Mathematics). 615 0$aNumerical analysis. 615 14$aOptimization. 615 24$aAnalysis. 615 24$aNumerical Analysis. 676 $a515.64 700 $aDontchev$b Asen L$4aut$4http://id.loc.gov/vocabulary/relators/aut$0308174 702 $aRockafellar$b R. Tyrrell$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299990603321 996 $aImplicit functions and solution mappings$91576310 997 $aUNINA