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Robust Linear Optimization
Aharon Ben-Tal, Laurent El Ghaoui, Arkadi Nemirovski
Copyright © 2009 by Princeton University Press
**PART I. ROBUST LINEAR OPTIMIZATION**
Chapter 1: Uncertain Linear Optimization Problems and their Robust Counterparts
- Data uncertainty in linear optimization (Section 1.1)
- Definition of uncertain linear problems and robust counterparts (Sections 1.2, 1.3)
- Non-affine perturbations and exercises (Sections 1.4 - 1.6)
Chapter 2: Robust Counterpart Approximations of Scalar Chance Constraints
- Specifying uncertainty sets and chance constraints (Section 2.1, 2.2)
- Basic examples with safe tractable approximations (Section 2.3)
- Extensions to more complex scenarios (Sections 2.4 - 2.6)
Chapter 3: Globalized Robust Counterparts of Uncertain LO Problems
- Motivation and definition for globalized robust counterparts (GRC)
- Computational tractability, example with antenna array synthesis (Sections 3.1 - 3.3)
- Exercises and notes (Section 3.4 - 3.5)
Chapter 4: More on Safe Tractable Approximations of Scalar Chance Constraints
- Robust counterpart representation for safe convex approximations to chance constraints
- Bernstein approximation, conditional value at risk, majorization techniques (Sections 4.1 - 4.6)
**PART II. ROBUST CONIC OPTIMIZATION**
Chapter 5: Uncertain Conic Optimization Concepts
- Preliminaries and tractability of robust counterparts for conic problems (Section 5.2)
Chapter 6: Solvable Cases in Uncertain Conic Quadratic Problems with Tractable RCs
- Scenario uncertainty, simple interval uncertainty, unstructured norm-bounded uncertainty cases
Chapter 7: Approximating Robust Counterparts of Uncertain Conic Quadratic Problems
- Structured and ∩-ellipsoidal uncertainties (Sections 7.1 - 7.3)
Chapter 8: Tractable RCs for Uncertain Semidefinite Problems
- Definition, tractability analysis
**PART IV. SELECTED APPLICATIONS**
Chapter 15: Selected Applications of Robust Optimization Techniques
- Examples in linear regression, inventory management, supply chain control (Sections 15.1 - 15.3)
Appendices:
A) Notation and prerequisites for conic programming
B) Auxiliary proofs for chapters 4 & 10
C) Solutions to selected exercises throughout the book
Bibliography
Index
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