LEADER 05362nam 22007575 450 001 9910728387903321 005 20240129144114.0 010 $a3-031-26790-7 024 7 $a10.1007/978-3-031-26790-1 035 $a(MiAaPQ)EBC7253745 035 $a(Au-PeEL)EBL7253745 035 $a(OCoLC)1381337046 035 $a(DE-He213)978-3-031-26790-1 035 $a(PPN)270613072 035 $a(CKB)26792018700041 035 $a(EXLCZ)9926792018700041 100 $a20230527d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aIntroduction to Methods for Nonlinear Optimization /$fby Luigi Grippo, Marco Sciandrone 205 $a1st ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2023. 215 $a1 online resource (721 pages) 225 1 $aLa Matematica per il 3+2,$x2038-5757 ;$v152 311 08$aPrint version: Grippo, Luigi Introduction to Methods for Nonlinear Optimization Cham : Springer International Publishing AG,c2023 9783031267895 320 $aIncludes bibliographical references and index. 327 $a1 Introduction.-2 Fundamental definitions and basic existence results -- 3 Optimality conditions for unconstrained problems in Rn -- 4 Optimality conditions for problems with convex feasible set -- 5 Optimality conditions for Nonlinear Programming -- 6 Duality theory -- 7 Optimality conditions based on theorems of the alternative -- 8 Basic concepts on optimization algorithms -- 9 Unconstrained optimization algorithms -- 10 Line search methods -- 11 Gradient method -- 12 Conjugate direction methods -- 13 Newton?s method -- 14 Trust region methods -- 15 Quasi-Newton Methods -- 16 Methods for nonlinear equations -- 17 Methods for least squares problems -- 18 Methods for large-scale optimization -- 19 Derivative-free methods for unconstrained optimization -- 20 Methods for problems with convex feasible set -- 21 Penalty and augmented Lagrangian methods -- 22 SQP methods -- 23 Introduction to interior point methods -- 24 Nonmonotone methods -- 25 Spectral gradient methods -- 26 Decomposition methods -- Appendix A: basic concepts of linear algebra and analysis -- Appendix B: Differentiation in Rn -- Appendix C: Introduction to convex analysis. 330 $aThis book has two main objectives: ? to provide a concise introduction to nonlinear optimization methods, which can be used as a textbook at a graduate or upper undergraduate level; ? to collect and organize selected important topics on optimization algorithms, not easily found in textbooks, which can provide material for advanced courses or can serve as a reference text for self-study and research. The basic material on unconstrained and constrained optimization is organized into two blocks of chapters: ? basic theory and optimality conditions ? unconstrained and constrained algorithms. These topics are treated in short chapters that contain the most important results in theory and algorithms, in a way that, in the authors? experience, is suitable for introductory courses. A third block of chapters addresses methods that are of increasing interest for solving difficult optimization problems. Difficulty can be typically due to the high nonlinearity of the objective function, ill-conditioning of the Hessian matrix, lack of information on first-order derivatives, the need to solve large-scale problems. In the book various key subjects are addressed, including: exact penalty functions and exact augmented Lagrangian functions, non monotone methods, decomposition algorithms, derivative free methods for nonlinear equations and optimization problems. The appendices at the end of the book offer a review of the essential mathematical background, including an introduction to convex analysis that can make part of an introductory course. 410 0$aLa Matematica per il 3+2,$x2038-5757 ;$v152 606 $aMathematical optimization 606 $aOperations research 606 $aComputer science?Mathematics 606 $aEngineering mathematics 606 $aEngineering?Data processing 606 $aContinuous Optimization 606 $aOperations Research and Decision Theory 606 $aMathematics of Computing 606 $aMathematical and Computational Engineering Applications 606 $aOptimització matemàtica$2thub 606 $aTeories no lineals$2thub 608 $aLlibres electrònics$2thub 615 0$aMathematical optimization. 615 0$aOperations research. 615 0$aComputer science?Mathematics. 615 0$aEngineering mathematics. 615 0$aEngineering?Data processing. 615 14$aContinuous Optimization. 615 24$aOperations Research and Decision Theory. 615 24$aMathematics of Computing. 615 24$aMathematical and Computational Engineering Applications. 615 7$aOptimització matemàtica 615 7$aTeories no lineals 676 $a519.3 676 $a530.15 700 $aGrippo$b Luigi$017752 702 $aSciandrone$b Marco 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910728387903321 996 $aIntroduction to Methods for Nonlinear Optimization$93398598 997 $aUNINA