An optimization primer / / Johannes O. Royset and Roger J.-B. Wets

• Record Nr.: UNISA996466550103316
• Autore: Royset Johannes O.
• Pubbl/distr/stampa: Cham, Switzerland : , : Springer, , [2022]; ©2022
• ISBN: 3-030-76275-0
• Descrizione fisica: 1 online resource (692 pages)
• Collana: Springer Series in Operations Research and Financial Engineering
• Disciplina: 519.6
• Soggetti: Optimització matemàtica; Mathematical optimization; Llibres electrònics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Intro -- Preface -- How to Read the Book -- Supporting Material -- Acknowledgements -- Contents -- 1 PRELUDE -- 1.A The Mathematical Curtain Rise -- 1.B Data Smoothing -- 1.C Optimization under Uncertainty -- 1.D Convex Analysis -- 1.E Estimation and Classification -- 1.F Gradient Descent Method -- 1.G Newton's Method -- 1.H Acceleration and Regularization -- 1.I Quasi-Newton Methods -- 1.J Coordinate Descent Algorithms -- 2 CONVEX OPTIMIZATION -- 2.A Formulations -- 2.B Subderivatives and Subgradients -- 2.C Subgradient Calculus -- 2.D Proximal Gradient Methods -- 2.E Linear Constraints -- 2.F Karush-Kuhn-Tucker Condition -- 2.G Interior-Point Method -- 2.H Support Vector Machines -- 2.I Subgradient Method -- 2.J Conic Constraints -- 2.K Polyhedral Analysis -- 3 OPTIMIZATION UNDER UNCERTAINTY -- 3.A Product Mix Optimization -- 3.B Expectation Functions -- 3.C Risk Modeling -- 3.D Models of Uncertainty -- 3.E Risk-Adaptive Design -- 3.F Optimality in Stochastic Optimization -- 3.G Stochastic Gradient Descent -- 3.H Simple Recourse Problems -- 3.I Control of Water Pollution -- 3.J Linear Recourse Problems -- 3.K Network Capacity Expansion -- 4 MINIMIZATION PROBLEMS -- 4.A Formulations -- 4.B Network Design and Operation -- 4.C Epigraphical Approximation Algorithm -- 4.D Constraint Softening -- 4.E Set Analysis -- 4.F Robotic Path Planning -- ; 4.G Tangent and Normal Cones I -- 4.H Tangent and Normal Cones II -- 4.I Subdifferentiability -- 4.J Optimality Conditions -- 4.K SQP and Interior-Point Methods -- 5 PERTURBATION AND DUALITY -- 5.A Rockafellians -- 5.B Quantitative Stability -- 5.C Lagrangians and Dual Problems -- 5.D Lagrangian Relaxation -- 5.E Saddle Points -- 5.F Strong Duality -- 5.G Reformulations -- 5.H L-Shaped Method -- 5.I Monitoring Functions -- 5.J Lagrangian Finite-Generation Method -- 6 WITHOUT CONVEXITY OR SMOOTHNESS.; 6.A Second-Order Analysis -- 6.B Augmented Lagrangians -- 6.C Epigraphical Nesting -- 6.D Optimality Conditions -- 6.E Sup-Projections -- 6.F Proximal Composite Method -- 6.G Design of Multi-Component Systems -- 6.H Difference-of-Convex Functions -- 6.I DC in Regression and Classification -- 6.J Approximation Errors -- 7 GENERALIZED EQUATIONS -- 7.A Formulations -- 7.B Equilibrium in Energy Markets -- 7.C Traffic Equilibrium -- 7.D Reformulation as Minimization Problems -- 7.E Projection Methods -- 7.F Nonsmooth Newton-Raphson Algorithm -- 7.G Continuity of Set-Valued Mappings -- 7.H Graphical Approximation Algorithm -- 7.I Consistent Approximations -- 7.J Approximation Errors -- 8 RISK MODELING AND SAMPLE AVERAGES -- 8.A Estimation of Optimality Gaps -- 8.B Risk and Regret -- 8.C Risk-Adaptive Data Analytics -- 8.D Duality -- 8.E Subgradients of Functionals -- 8.F Residual Risk and Surrogates -- 8.G Sample Average Approximations -- 8.H Concentration Inequalities -- 8.I Diametrical Stochastic Optimization -- 9 GAMES AND MINSUP PROBLEMS -- 9.A Nash Games -- 9.B Formulation as Minsup Problems -- 9.C Bifunctions and Solutions -- 9.D Lopsided Approximation Algorithm -- 9.E Lop-Convergence I -- 9.F Lop-Convergence II -- 9.G Approximation of Games -- 9.H Walras Barter Model -- 10 DECOMPOSITION -- 10.A Proximal Alternating Gradient Method -- 10.B Linkage Constraints -- 10.C Progressive Decoupling Algorithm -- 10.D Local Elicitation -- 10.E Decoupling in Stochastic Optimization -- 10.F Strong Monotonicity -- 10.G Variational Convexity and Elicitation -- 10.H Nonlinear Linkage -- References -- Index.