Robust optimization / Aharon Ben-Tal, Laurent El Ghaoui, Arkadi Nemirovski.

Format:

Book

Author/Creator:

Ben-Tal, A.

Contributor:

El Ghaoui, Laurent.

Nemirovskiĭ, A. S. (Arkadiĭ Semenovich)

Series:

Princeton Series in Applied Mathematics

Princeton Series in Applied Mathematics ; 28

Language:

English

Subjects (All):

Robust optimization.

Linear programming.

Physical Description:

1 online resource (565 p.)

Edition:

Course Book

Place of Publication:

Princeton, NJ : Princeton University Press, c2009.

Language Note:

English

Summary:

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.

Contents:

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

Notes:

Description based upon print version of record.

ISBN:

9786612259289

9781282259287

1282259288

9781400831050

1400831059

OCLC:

439040007