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. Readers will find coverage of the basic concepts of modeling these problems, including recourse actions and the nonanticipativity principle. The book also includes the theory of two-stage and multistage stochastic programming problems; the current state of the theory on chance (probabilistic) constraints, including the structure of the problems, optimality theory, and duality; and statistical inference in and risk-averse approaches to stochastic programming.

Lectures on Stochastic Programming: Modeling and Theory (MPS-SIAM Series on Optimization)

Science & Math

Alexander Shapiro

Darinka Dentcheva

Andrzej Ruszczynski

Mathematics

Society for Industrial and Applied Mathematics

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Blond's Property

Neil C. Blond

Yoran Chen

John Marafino

Jonathan A. Tyler

SULZBURGER & GRAHAM

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.

Lectures on Stochastic Programming: Modeling and Theory, Second Edition

SIAM: Society for Industrial and Applied Mathematics

Lectures on Stochastic Programming: Modeling and Theory, Third Edition covers optimization problems involving uncertain parameters for which stochastic models are available. These problems occur in almost all areas of science and engineering. This substantial revision of the previous edition presents a modern theory of stochastic programming, including expanded coverage of sample complexity, risk measures, and distributionally robust optimization: • Chapter 6 is updated and the interchangeability principle for risk measures is discussed in detail. • Two new chapters, Distributionally Robust Stochastic Programming (DRSP) and Computational Methods provide readers with a solid understanding of emerging topics. • Chapter 8 presents new material on formulation and numerical approaches to solving periodical multistage stochastic programs. This book is written for researchers and graduate students working on theory and applications of optimization.

Lectures on Stochastic Programming: Modeling and Theory, Third Edition

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