eBook

Robust Optimization

Nemirovski, Arkadi, El Ghaoui, Laurent, Ben-Tal, Aharon

2009

Overview

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.

• Publisher: Princeton University Press
• Subject: Accuracy and precision / Additive model / Almost surely / Approximation / Approximation algorithm / Best / Big O notation / Candidate solution / Central limit theorem / Chaos theory / Coefficient / Computational complexity theory / Convex optimization / Curse of dimensionality / Decision problem / Decision rule / Degeneracy (mathematics) / Diagram (category theory) / Duality (optimization) / Dynamic programming / Feasible region / For All Practical Purposes / General Topics for Engineers / Identity matrix / Inequality (mathematics) / Infimum and supremum / Law of large numbers / Linear dynamical system / Linear inequality / Linear map / Linear matrix inequality / Linear programming / Loss function / Markov chain / Mathematical optimization / MATHEMATICS / MATHEMATICS / Applied / MATHEMATICS / Linear & Nonlinear Programming / Mathematische Optimierung / Maxima and minima / Norm (mathematics) / Normal distribution / NP-hardness / Optimal control / Optimization problem / Pairwise / Parameter / Parametric family / Probability / Probability distribution / Quantity / Relative interior / Robust control / Robust decision-making / Robust optimization / Robustes Verfahren / Sensitivity analysis / Simple set / Singular value / Slack variable / Special case / Spherical model / Spline (mathematics) / Stochastic / Stochastic optimization / Stochastic programming / Strong duality / Theorem / Theorie / Time complexity / Uncertainty / Upper and lower bounds / Variable (mathematics) / Virtual displacement / Weak duality / With high probability / worst and average case
• ISBN: 9780691143682, 0691143684, 9781400831050, 1400831059