Optimization problems involving stochastic models occur in most areas of science and engineering, particularly telecommunications, medicine, and finance. Their existence reveals a need for rigorous ways of formulating, analyzing, and solving such problems. This book focuses on optimization problems involving uncertain parameters and covers the theoretical foundations and recent advances in areas where stochastic models are available. In this second edition, the authors introduce new material to reflect recent developments, including: analytical descriptions of the tangent and normal cones of chance constrained sets; analysis of optimality conditions for nonconvex problems; a discussion of the stochastic dual dynamic programming method; an extended discussion of law invariant coherent risk measures and their Kusuoka representations; and an in-depth analysis of dynamic risk measures and concepts of time consistency, including several new results. This book is intended for researchers working in optimization. It is also suitable for advanced graduate courses in this area.
Alexander Shapiro is a Professor in the School of Industrial and Systems Engineering at Georgia Institute of Technology. He has published more than 100 articles and is the co-author of several books. Darinka Dentcheva is a Professor of Mathematics at Stevens Institute of Technology. She works in the areas of decisions under uncertainty, convex analysis, and stability of optimization problems. Andrzej Ruszczynski is a Professor of Operations Research at Rutgers University. His research is devoted to the theory and methods of optimization under uncertainty and risk.
List of notations; Preface to the second edition; Preface to the first edition; 1. Stochastic programming models; 2. Two-stage problems; 3. Multistage problems; 4. Optimization models with probabilistic constraints; 5. Statistical inference; 6. Risk averse optimization; 7. Background material; 8. Bibliographical remarks; Bibliography; Index.