Lectures on Stochastic Programming: Modeling and Theory, Second Edition
by Alexander Shapiro
Publisher: SIAM - Society for Industrial and Applied Mathematics
Edition: Second - 2014
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.