Darinka Dentcheva - Böcker

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.

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.

This book offers a comprehensive presentation of the theory and methods of risk-averse optimization and control. Problems of this type arise in finance, energy production and distribution, supply chain management, medicine, and many other areas, where not only the average performance of a stochastic system is essential, but also high-impact and low-probability events must be taken into account. The book is a self-contained presentation of the utility theory, the theory of measures of risk, including systemic and dynamic measures of risk, and their use in optimization and control models. It also covers stochastic dominance relations and their application as constraints in optimization models. Optimality conditions for problems with nondifferentiable and nonconvex functions and operators involving risk measures and stochastic dominance relations are discussed. Much attention is paid to multi-stage risk-averse optimization problems and to risk-averse Markov decision problems. Specialized algorithms for solving risk-averse optimization and control problems are presented and analyzed: stochastic subgradient methods for risk optimization, decomposition methods for dynamic problems, event cut and dual methods for stochastic dominance constraints, and policy iteration methods for control problems. The target audience is researchers and graduate students in the areas of mathematics, business analytics, insurance and finance, engineering, and computer science. The theoretical considerations are illustrated with examples, which make the book useful material for advanced courses in the area.