LEADER 05356nam 22007335 450 001 9911001787603321 005 20250506125928.0 010 $a3-031-84837-3 024 7 $a10.1007/978-3-031-84837-7 035 $a(CKB)38753876500041 035 $a(DE-He213)978-3-031-84837-7 035 $a(MiAaPQ)EBC32256093 035 $a(Au-PeEL)EBL32256093 035 $a(OCoLC)1534199136 035 $a(EXLCZ)9938753876500041 100 $a20250506d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMethods of Nonsmooth Optimization in Stochastic Programming $eFrom Conceptual Algorithms to Real-World Applications /$fby Wim Stefanus van Ackooij, Welington Luis de Oliveira 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (XVI, 570 p. 39 illus., 30 illus. in color.) 225 1 $aInternational Series in Operations Research & Management Science,$x2214-7934 ;$v363 311 08$a3-031-84836-5 327 $aIntroduction -- Primer of convex analysis -- Variational analysis -- Linear and nonlinear optimization problems -- Probability and Statistics -- Fundamental modeling questions in stochastic programming -- Adjusting to uncertainty: modeling recourse -- Probability constraints -- Proximal point algorithms for problems with structure -- Cutting-plane algorithms for nonsmooth convex optimization over simple domains -- Bundle methods for nonsmooth convex optimization over simple domains -- Methods for nonlinearly constrained nonsmooth optimization problems -- Methods for nonsmooth optimization with mixed-integer variables -- Methods for nonsmooth nonconvex optimization -- Two-stage stochastic programs -- Progressive decoupling in multistage stochastic programming -- Scenario decomposition with alternating projections -- Methods for multistage stochastic linear programs -- Methods for handling probability. 330 $aThis book presents a comprehensive series of methods in nonsmooth optimization, with a particular focus on their application in stochastic programming and dedicated algorithms for decision-making under uncertainty. Each method is accompanied by rigorous mathematical analysis, ensuring a deep understanding of the underlying principles. The theoretical discussions included are essential for comprehending the mechanics of various algorithms and the nature of the solutions they provide?whether they are global, local, stationary, or critical. The book begins by introducing fundamental tools from set-valued analysis, optimization, and probability theory. It then transitions from deterministic to stochastic optimization, starting with a thorough discussion of modeling, understanding uncertainty, and incorporating it into optimization problems. Following this foundation, the book explores numerical algorithms for nonsmooth optimization, covering well-known decomposition techniques and algorithms for convex optimization, mixed-integer convex programming, and nonconvex optimization. Additionally, it introduces numerical algorithms specifically for stochastic programming, focusing on stochastic programming with recourse, chance-constrained optimization, and detailed algorithms for both risk-neutral and risk-averse multistage stochastic programs. The book guides readers through the entire process, from defining optimization models for practical problems to presenting implementable algorithms that can be applied in practice. It is intended for students, practitioners, and scholars who may be unfamiliar with stochastic programming and nonsmooth optimization. The analyses provided are also valuable for practitioners who may not be interested in convergence proofs but wish to understand the nature of the solutions obtained. 410 0$aInternational Series in Operations Research & Management Science,$x2214-7934 ;$v363 606 $aOperations research 606 $aMathematical optimization 606 $aManagement science 606 $aNumerical analysis 606 $aStochastic processes 606 $aCalculus 606 $aOperations Research and Decision Theory 606 $aOptimization 606 $aOperations Research, Management Science 606 $aNumerical Analysis 606 $aContinuous Optimization 606 $aStochastic Calculus 615 0$aOperations research. 615 0$aMathematical optimization. 615 0$aManagement science. 615 0$aNumerical analysis. 615 0$aStochastic processes. 615 0$aCalculus. 615 14$aOperations Research and Decision Theory. 615 24$aOptimization. 615 24$aOperations Research, Management Science. 615 24$aNumerical Analysis. 615 24$aContinuous Optimization. 615 24$aStochastic Calculus. 676 $a658.403 700 $avan Ackooij$b Wim Stefanus$4aut$4http://id.loc.gov/vocabulary/relators/aut$01821068 702 $ade Oliveira$b Welington Luis$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911001787603321 996 $aMethods of Nonsmooth Optimization in Stochastic Programming$94384479 997 $aUNINA