Lectures on Stochastic Programming: Modeling and Theory

Optimization problems involving stochastic models occur in almost all areas of science and engineering, such as telecommunications, medicine, and finance. Their existence compels 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 Lectures on Stochastic Programming: Modeling and Theory, Second Edition, the authors introduce new material to reflect recent developments in stochastic programming, including: an analytical description of the tangent and normal cones of chance constrained sets; analysis of optimality conditions applied to 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 in-depth analysis of dynamic risk measures and concepts of time consistency, including several new results.

Audience: This book is intended for researchers working on theory and applications of optimization. It also is suitable as a text for advanced graduate courses in optimization.

Contents: List of Notations; Preface to the Second Edition; Preface to the First Edition; Chapter 1: Stochastic Programming Models; Chapter 2: Two-Stage Problems; Chapter 3: Multistage Problems; Chapter 4: Optimization Models with Probabilistic Constraints; Chapter 5: Statistical Inference; Chapter 6: Risk Averse Optimization; Chapter 7: Background Material; Chapter 8: Bibliographical Remarks; Bibliography; Index.

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 in peer-reviewed journals and is the coauthor 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.