LEADER 03673nam 22005415 450 001 9910300121803321 005 20251116204058.0 010 $a3-319-91578-9 024 7 $a10.1007/978-3-319-91578-4 035 $a(CKB)4100000007158932 035 $a(DE-He213)978-3-319-91578-4 035 $a(MiAaPQ)EBC6315309 035 $a(PPN)232471584 035 $a(EXLCZ)994100000007158932 100 $a20181119d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLectures on Convex Optimization /$fby Yurii Nesterov 205 $a2nd ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (XXIII, 589 p. 1 illus.) 225 1 $aSpringer Optimization and Its Applications,$x1931-6828 ;$v137 311 08$a3-319-91577-0 327 $aIntroduction -- Part I Black-Box Optimization -- 1 Nonlinear Optimization -- 2 Smooth Convex Optimization -- 3 Nonsmooth Convex Optimization -- 4 Second-Order Methods -- Part II Structural Optimization -- 5 Polynomial-time Interior-Point Methods -- 6 Primal-Dual Model of Objective Function -- 7 Optimization in Relative Scale -- Bibliographical Comments -- Appendix A. Solving some Auxiliary Optimization Problems -- References -- Index. 330 $aThis book provides a comprehensive, modern introduction to convex optimization, a field that is becoming increasingly important in applied mathematics, economics and finance, engineering, and computer science, notably in data science and machine learning. Written by a leading expert in the field, this book includes recent advances in the algorithmic theory of convex optimization, naturally complementing the existing literature. It contains a unified and rigorous presentation of the acceleration techniques for minimization schemes of first- and second-order. It provides readers with a full treatment of the smoothing technique, which has tremendously extended the abilities of gradient-type methods. Several powerful approaches in structural optimization, including optimization in relative scale and polynomial-time interior-point methods, are also discussed in detail. Researchers in theoretical optimization as well as professionals working on optimization problems will find this book very useful. It presents many successful examples of how to develop very fast specialized minimization algorithms. Based on the author?s lectures, it can naturally serve as the basis for introductory and advanced courses in convex optimization for students in engineering, economics, computer science and mathematics. 410 0$aSpringer Optimization and Its Applications,$x1931-6828 ;$v137 606 $aMathematical optimization 606 $aAlgorithms 606 $aOptimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26008 606 $aAlgorithm Analysis and Problem Complexity$3https://scigraph.springernature.com/ontologies/product-market-codes/I16021 606 $aAlgorithms$3https://scigraph.springernature.com/ontologies/product-market-codes/M14018 615 0$aMathematical optimization. 615 0$aAlgorithms. 615 14$aOptimization. 615 24$aAlgorithm Analysis and Problem Complexity. 615 24$aAlgorithms. 676 $a519.3 700 $aNesterov$b I?U?. E.$4aut$4http://id.loc.gov/vocabulary/relators/aut$0535744 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300121803321 996 $aLectures on Convex Optimization$92057008 997 $aUNINA