Robust optimization [[electronic resource] /] / Aharon Ben-Tal, Laurent El Ghaoui, Arkadi Nemirovski

• Autore: Ben-Tal A
• Pubblicazione: Princeton, NJ, : Princeton University Press, c2009
• Edizione: Course Book
• Descrizione fisica: 1 online resource (565 p.)
• Disciplina: 519.6
• Soggetto topico: Robust optimization; Linear programming
• Soggetto non controllato: 0O; Accuracy and precision; Additive model; Almost surely; Approximation algorithm; Approximation; Best, worst and average case; Bifurcation theory; Big O notation; Candidate solution; Central limit theorem; Chaos theory; Coefficient; Computational complexity theory; Constrained optimization; Convex hull; Convex optimization; Convex set; Cumulative distribution function; Curse of dimensionality; Decision problem; Decision rule; Degeneracy (mathematics); Diagram (category theory); Duality (optimization); Dynamic programming; Exponential function; Feasible region; Floor and ceiling functions; For All Practical Purposes; Free product; Ideal solution; Identity matrix; Inequality (mathematics); Infimum and supremum; Integer programming; Law of large numbers; Likelihood-ratio test; Linear dynamical system; Linear inequality; Linear map; Linear matrix inequality; Linear programming; Linear regression; Loss function; Margin classifier; Markov chain; Markov decision process; Mathematical optimization; Max-plus algebra; Maxima and minima; Multivariate normal distribution; NP-hardness; Norm (mathematics); Normal distribution; Optimal control; Optimization problem; Orientability; P versus NP problem; Pairwise; Parameter; Parametric family; Probability distribution; Probability; Proportionality (mathematics); Quantity; Random variable; Relative interior; Robust control; Robust decision-making; Robust optimization; Semi-infinite; Sensitivity analysis; Simple set; Singular value; Skew-symmetric matrix; Slack variable; Special case; Spherical model; Spline (mathematics); State variable; Stochastic calculus; Stochastic control; Stochastic optimization; Stochastic programming; Stochastic; Strong duality; Support vector machine; Theorem; Time complexity; Uncertainty; Uniform distribution (discrete); Unimodality; Upper and lower bounds; Variable (mathematics); Virtual displacement; Weak duality; Wiener filter; With high probability; Without loss of generality
• Classificazione: SK 870
• Altri autori: El GhaouiLaurent NemirovskiĭArkadiĭ Semenovich
• Note generali: Description based upon print version of record.
• Nota di contenuto: Frontmatter -- Contents -- Preface -- Part I. Robust Linear Optimization -- Chapter One. Uncertain Linear Optimization Problems and their Robust Counterparts -- Chapter Two. Robust Counterpart Approximations of Scalar Chance Constraints -- Chapter Three. Globalized Robust Counterparts of Uncertain LO Problems -- Chapter Four. More on Safe Tractable Approximations of Scalar Chance Constraints -- Part II. Robust Conic Optimization -- Chapter Five. Uncertain Conic Optimization: The Concepts -- Chapter Six. Uncertain Conic Quadratic Problems with Tractable RCs -- Chapter Seven. Approximating RCs of Uncertain Conic Quadratic Problems -- Chapter Eight. Uncertain Semidefinite Problems with Tractable RCs -- Chapter Nine. Approximating RCs of Uncertain Semidefinite Problems -- Chapter Ten. Approximating Chance Constrained CQIs and LMIs -- Chapter Eleven. Globalized Robust Counterparts of Uncertain Conic Problems -- Chapter Twelve. Robust Classi¯cation and Estimation -- Part III. Robust Multi-Stage Optimization -- Chapter Thirteen. Robust Markov Decision Processes -- Chapter Fourteen. Robust Adjustable Multistage Optimization -- Part IV. Selected Applications -- Chapter Fifteen. Selected Applications -- Appendix A: Notation and Prerequisites -- Appendix B: Some Auxiliary Proofs -- Appendix C: Solutions to Selected Exercises -- Bibliography -- Index
• Sommario/riassunto: Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such problems today without considering this powerful methodology. Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the first book to provide a comprehensive and up-to-date account of the subject. Robust optimization is designed to meet some major challenges associated with uncertainty-affected optimization problems: to operate under lack of full information on the nature of uncertainty; to model the problem in a form that can be solved efficiently; and to provide guarantees about the performance of the solution. The book starts with a relatively simple treatment of uncertain linear programming, proceeding with a deep analysis of the interconnections between the construction of appropriate uncertainty sets and the classical chance constraints (probabilistic) approach. It then develops the robust optimization theory for uncertain conic quadratic and semidefinite optimization problems and dynamic (multistage) problems. The theory is supported by numerous examples and computational illustrations. An essential book for anyone working on optimization and decision making under uncertainty, Robust Optimization also makes an ideal graduate textbook on the subject.
• Titolo autorizzato: Robust optimization
• ISBN: 1-282-25928-8; 9786612259289; 1-4008-3105-9
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910778219003321
• Lo trovi qui: Univ. Federico II
• Serie: Princeton Series in Applied Mathematics