Cover -- Title -- Copyright -- Contents -- Preface -- PART I. ROBUST LINEAR OPTIMIZATION -- Chapter 1. Uncertain Linear Optimization Problems and their Robust Counterparts -- 1.1 Data Uncertainty in Linear Optimization -- 1.2 Uncertain Linear Problems and their Robust Counterparts -- 1.3 Tractability of Robust Counterparts -- 1.4 Non-Affine Perturbations -- 1.5 Exercises -- 1.6 Notes and Remarks -- Chapter 2. Robust Counterpart Approximations of Scalar Chance Constraints -- 2.1 How to Specify an Uncertainty Set -- 2.2 Chance Constraints and their Safe Tractable Approximations -- 2.3 Safe Tractable Approximations of Scalar Chance Constraints: Basic Examples -- 2.4 Extensions -- 2.5 Exercises -- 2.6 Notes and Remarks -- Chapter 3. Globalized Robust Counterparts of Uncertain LO Problems -- 3.1 Globalized Robust Counterpart-Motivation and Definition -- 3.2 Computational Tractability of GRC -- 3.3 Example: Synthesis of Antenna Arrays -- 3.4 Exercises -- 3.5 Notes and Remarks -- Chapter 4. More on Safe Tractable Approximations of Scalar Chance Constraints -- 4.1 Robust Counterpart Representation of a Safe Convex Approximation to a Scalar Chance Constraint -- 4.2 Bernstein Approximation of a Chance Constraint -- 4.3 From Bernstein Approximation to Conditional Value at Risk and Back -- 4.4 Majorization -- 4.5 Beyond the Case of Independent Linear Perturbations -- 4.6 Exercises -- 4.7 Notes and Remarks -- PART II. ROBUST CONIC OPTIMIZATION -- Chapter 5. Uncertain Conic Optimization: The Concepts -- 5.1 Uncertain Conic Optimization: Preliminaries -- 5.2 Robust Counterpart of Uncertain Conic Problem: Tractability -- 5.3 Safe Tractable Approximations of RCs of Uncertain Conic Inequalities -- 5.4 Exercises -- 5.5 Notes and Remarks -- Chapter 6. Uncertain Conic Quadratic Problems with Tractable RCs -- 6.1 A Generic Solvable Case: Scenario Uncertainty.

6.2 Solvable Case I: Simple Interval Uncertainty -- 6.3 Solvable Case II: Unstructured Norm-Bounded Uncertainty -- 6.4 Solvable Case III: Convex Quadratic Inequality with Unstructured Norm-Bounded Uncertainty -- 6.5 Solvable Case IV: CQI with Simple Ellipsoidal Uncertainty -- 6.6 Illustration: Robust Linear Estimation -- 6.7 Exercises -- 6.8 Notes and Remarks -- Chapter 7. Approximating RCs of Uncertain Conic Quadratic Problems -- 7.1 Structured Norm-Bounded Uncertainty -- 7.2 The Case of ∩-Ellipsoidal Uncertainty -- 7.3 Exercises -- 7.4 Notes and Remarks -- Chapter 8. Uncertain Semidefinite Problems with Tractable RCs -- 8.1 Uncertain Semidefinite Problems -- 8.2 Tractability of RCs of Uncertain Semidefinite Problems -- 8.3 Exercises -- 8.4 Notes and Remarks -- Chapter 9. Approximating RCs of Uncertain Semidefinite Problems -- 9.1 Tight Tractable Approximations of RCs of Uncertain SDPs with Structured Norm-Bounded Uncertainty -- 9.2 Exercises -- 9.3 Notes and Remarks -- Chapter 10. Approximating Chance Constrained CQIs and LMIs -- 10.1 Chance Constrained LMIs -- 10.2 The Approximation Scheme -- 10.3 Gaussian Majorization -- 10.4 Chance Constrained LMIs: Special Cases -- 10.5 Notes and Remarks -- Chapter 11. Globalized Robust Counterparts of Uncertain Conic Problems -- 11.1 Globalized Robust Counterparts of Uncertain Conic Problems: Definition -- 11.2 Safe Tractable Approximations of GRCs -- 11.3 GRC of Uncertain Constraint: Decomposition -- 11.4 Tractability of GRCs -- 11.5 Illustration: Robust Analysis of Nonexpansive Dynamical Systems -- Chapter 12. Robust Classification and Estimation -- 12.1 Robust Support Vector Machines -- 12.2 Robust Classification and Regression -- 12.3 Affine Uncertainty Models -- 12.4 Random Affine Uncertainty Models -- 12.5 Exercises -- 12.6 Notes and remarks -- PART III. ROBUST MULTI-STAGE OPTIMIZATION.

Chapter 13. Robust Markov Decision Processes -- 13.1 Markov Decision Processes -- 13.2 The Robust MDP Problems -- 13.3 The Robust Bellman Recursion on Finite Horizon -- 13.4 Notes and Remarks -- Chapter 14. Robust Adjustable Multistage Optimization -- 14.1 Adjustable Robust Optimization: Motivation -- 14.2 Adjustable Robust Counterpart -- 14.3 Affinely Adjustable Robust Counterparts -- 14.4 Adjustable Robust Optimization and Synthesis of Linear Controllers -- 14.5 Exercises -- 14.6 Notes and Remarks -- PART IV. SELECTED APPLICATIONS -- Chapter 15. Selected Applications -- 15.1 Robust Linear Regression and Manufacturing of TV Tubes -- 15.2 Inventory Management with Flexible Commitment Contracts -- 15.3 Controlling a Multi-Echelon Multi-Period Supply Chain -- Appendix A. Notation and Prerequisites -- A.1 Notation -- A.2 Conic Programming -- A.3 Efficient Solvability of Convex Programming -- Appendix B. Some Auxiliary Proofs -- B.1 Proofs for Chapter 4 -- B.2 S-Lemma -- B.3 Approximate S-Lemma -- B.4 Matrix Cube Theorem -- B.5 Proofs for Chapter 1 -- Appendix C. Solutions to Selected Exercises -- C.1 Chapter 1 -- C.2 Chapter 2 -- C.3 Chapter 3 -- C.4 Chapter 4 -- C.5 Chapter 5 -- C.6 Chapter 6 -- C.7 Chapter 7 -- C.8 Chapter 8 -- C.9 Chapter 9 -- C.10 Chapter 12 -- C.11 Chapter 14 -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- I -- L -- M -- N -- P -- R -- S -- T -- U -- W.