Robust Optimization

✍ Scribed by Aharon Ben-Tal; Laurent El Ghaoui; Arkadi Nemirovski

• Publisher: Princeton University Press
• Year: 2009
• Tongue: English
• Leaves: 564
• Series: Princeton Series in Applied Mathematics; 28
• Edition: Course Book
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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