Robust Optimization

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9780691143682: Robust Optimization

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.

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Recensione:

"Robust optimization is an active area of research that is likely to find many practical applications in the future. This book is an authoritative reference that will be very useful to researchers working in this area. Furthermore, the book has been structured so that the first part could easily be used as the text for a graduate level course in robust optimization." --Brian Borchers, MAA Reviews

"[T]his reference book gives an excellent and stimulating account of the classical and advanced results in the field, and should be consulted by all researchers and practitioners." --Joseph Frédéric Bonnans, Zentralblatt MATH

Contenuti:

Preface ix

PART I. ROBUST LINEAR OPTIMIZATION 1

Chapter 1. Uncertain Linear Optimization Problems and their Robust Counterparts 3
1.1 Data Uncertainty in Linear Optimization 3
1.2 Uncertain Linear Problems and their Robust Counterparts 7
1.3 Tractability of Robust Counterparts 16
1.4 Non-Affne Perturbations 23
1.5 Exercises 25
1.6 Notes and Remarks 25

Chapter 2. Robust Counterpart Approximations of Scalar Chance Constraints 27
2.1 How to Specify an Uncertainty Set 27
2.2 Chance Constraints and their Safe Tractable Approximations 28
2.3 Safe Tractable Approximations of Scalar Chance Constraints: Basic Examples 31
2.4 Extensions 44
2.5 Exercises 60
2.6 Notes and Remarks 64

Chapter 3. Globalized Robust Counterparts of Uncertain LO Problems 67
3.1 Globalized Robust Counterpart | Motivation and Definition 67
3.2 Computational Tractability of GRC 69
3.3 Example: Synthesis of Antenna Arrays 70
3.4 Exercises 79
3.5 Notes and Remarks 79

Chapter 4. More on Safe Tractable Approximations of Scalar Chance Constraints 81
4.1 Robust Counterpart Representation of a Safe Convex Approximation to a Scalar Chance Constraint 81
4.2 Bernstein Approximation of a Chance Constraint 83
4.3 From Bernstein Approximation to Conditional Value at Risk and Back 90
4.4 Majorization 105
4.5 Beyond the Case of Independent Linear Perturbations 109
4.6 Exercises 136
4.7 Notes and Remarks 145

PART II. ROBUST CONIC OPTIMIZATION 147

Chapter 5. Uncertain Conic Optimization: The Concepts 149
5.1 Uncertain Conic Optimization: Preliminaries 149
5.2 Robust Counterpart of Uncertain Conic Problem: Tractability 151
5.3 Safe Tractable Approximations of RCs of Uncertain Conic Inequalities 153
5.4 Exercises 156
5.5 Notes and Remarks 157

Chapter 6. Uncertain Conic Quadratic Problems with Tractable RCs 159
6.1 A Generic Solvable Case: Scenario Uncertainty 159
6.2 Solvable Case I: Simple Interval Uncertainty 160
6.3 Solvable Case II: Unstructured Norm-Bounded Uncertainty 161
6.4 Solvable Case III: Convex Quadratic Inequality with Un-structured Norm-Bounded Uncertainty 165
6.5 Solvable Case IV: CQI with Simple Ellipsoidal Uncertainty 167
6.6 Illustration: Robust Linear Estimation 173
6.7 Exercises 178
6.8 Notes and Remarks 178

Chapter 7. Approximating RCs of Uncertain Conic Quadratic Problems 179
7.1 Structured Norm-Bounded Uncertainty 179
7.2 The Case of \-Ellipsoidal Uncertainty 195
7.3 Exercises 201
7.4 Notes and Remarks 201

Chapter 8. Uncertain Semidefinite Problems with Tractable RCs 203
8.1 Uncertain Semidefinite Problems 203
8.2 Tractability of RCs of Uncertain Semidefinite Problems 204
8.3 Exercises 222
8.4 Notes and Remarks 222

Chapter 9. Approximating RCs of Uncertain Semide¯nite
Problems 225
9.1 Tight Tractable Approximations of RCs of Uncertain SDPs
with Structured Norm-Bounded Uncertainty 225
9.2 Exercises 232
9.3 Notes and Remarks 234

Chapter 10. Approximating Chance Constrained CQIs and LMIs 235
10.1 Chance Constrained LMIs 235
10.2 The Approximation Scheme 240
10.3 Gaussian Majorization 252
10.4 Chance Constrained LMIs: Special Cases 255
10.5 Notes and Remarks 276

Chapter 11. Globalized Robust Counterparts of Uncertain Conic Problems 279
11.1 Globalized Robust Counterparts of Uncertain Conic Problems: De¯nition 279
11.2 Safe Tractable Approximations of GRCs 281
11.3 GRC of Uncertain Constraint: Decomposition 282
11.4 Tractability of GRCs 284
11.5 Illustration: Robust Analysis of Nonexpansive Dynamical Systems 292

Chapter 12. Robust Classification and Estimation 301
12.1 Robust Support Vector Machines 301
12.2 Robust Classification and Regression 309
12.3 Affine Uncertainty Models 325
12.4 Random Affine Uncertainty Models 331
12.5 Exercises 336
12.6 Notes and remarks 337

PART III. ROBUST MULTI-STAGE OPTIMIZATION 339

Chapter 13. Robust Markov Decision Processes 341
13.1 Markov Decision Processes 341
13.2 The Robust MDP Problems 345
13.3 The Robust Bellman Recursion on Finite Horizon 347
13.4 Notes and Remarks 352

Chapter 14. Robust Adjustable Multistage Optimization 355
14.1 Adjustable Robust Optimization: Motivation 355
14.2 Adjustable Robust Counterpart 357
14.3 Affinely Adjustable Robust Counterparts 368
14.4 Adjustable Robust Optimization and Synthesis of Linear Controllers 392
14.5 Exercises 408
14.6 Notes and Remarks 411

PART IV. SELECTED APPLICATIONS 415

Chapter 15. Selected Applications 417
15.1 Robust Linear Regression and Manufacturing of TV Tubes 417
15.2 Inventory Management with Flexible Commitment Contracts 421
15.3 Controlling a Multi-Echelon Multi-Period Supply Chain 432

Appendix A. Notation and Prerequisites 447
A.1 Notation 447
A.2 Conic Programming 448
A.3 Efficient Solvability of Convex Programming 460
Appendix B. Some Auxiliary Proofs 469
B.1 Proofs for Chapter 4 469
B.2 S-Lemma 481
B.3 Approximate S-Lemma 483
B.4 Matrix Cube Theorem 489
B.5 Proofs for Chapter 10 506
Appendix C. Solutions to Selected Exercises 511
C.1 Chapter 1 511
C.2 Chapter 2 511
C.3 Chapter 3 513
C.4 Chapter 4 513
C.5 Chapter 5 516
C.6 Chapter 6 519
C.7 Chapter 7 520
C.8 Chapter 8 521
C.9 Chapter 9 523
C.10 Chapter 12 525
C.11 Chapter 14 527

Bibliography 531
Index 539

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Descrizione libro Princeton University Press. Hardback. Condizione libro: new. BRAND NEW, Robust Optimization, Aharon Ben-Tal, Laurent El Ghaoui, Arkadi Nemirovski, 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. Codice libro della libreria B9780691143682

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Descrizione libro Princeton University Press, United States, 2009. Hardback. Condizione libro: New. 251 x 185 mm. Language: English . Brand New Book. 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. Codice libro della libreria AAH9780691143682

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Descrizione libro Princeton University Press, United States, 2009. Hardback. Condizione libro: New. 251 x 185 mm. Language: English . Brand New Book. 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. Codice libro della libreria AAH9780691143682

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