Introduction to stochastic programming.
2nd ed.

*(English)*Zbl 1223.90001
Springer Series in Operations Research and Financial Engineering. New York, NY: Springer (ISBN 978-1-4614-0236-7/hbk; 978-1-4614-0237-4/ebook). xxv, 485 p. (2011).

This is a substantial extension of the acknowledged textbook; see Zbl 0892.90142 for a review of the first edition (1997).

The primary objective remains to help the students to understand how to model uncertainty into mathematical optimization problems, what uncertainty brings to the decision process and which techniques help to manage uncertainty in solving the problems. Accordingly, it covers in detail the main themes and methods of stochastic programming (model building, survey of basic theoretical properties, solution methods, approximation and sampling techniques). This edition deals in addition with recent topics of the focused interest in research and applications of stochastic programming such as new results on risk modeling, on Monte Carlo sampling methods and approximations, and clarifies relationships to other methods. An extended chapter on stochastic integer programming reflects advances in this field. Naturally, much care is devoted to various aspects of solution methods.

The book is aimed at researchers, master’s level and postgraduate students of mathematics and also of related applied disciplines, such as operations research, finance, management, and engineering. With references to original papers, the authors include (mostly without proofs) mathematically advanced themes, e.g., properties of expectation functionals, optimality conditions, convergence results, for which knowledge of convex analysis and of optimization theory is expected. On the other hand, the worked examples and numerous exercises delineate clearly the wide-ranging possibilities of applications of stochastic programming and, at the same time, they help to build an intuition how to model uncertainty within mathematical programs and how to interpret the obtained results. The book will thus certainly attract also the wide spectrum of readers whose main interest lies in possible exploitation of stochastic programming methodology and will help them to find their own way to treat actual problems using stochastic programming methods.

As a whole, the three main building blocks of stochastic programming – stochastic modeling, optimization, numerical methods – are well represented and balanced.

The primary objective remains to help the students to understand how to model uncertainty into mathematical optimization problems, what uncertainty brings to the decision process and which techniques help to manage uncertainty in solving the problems. Accordingly, it covers in detail the main themes and methods of stochastic programming (model building, survey of basic theoretical properties, solution methods, approximation and sampling techniques). This edition deals in addition with recent topics of the focused interest in research and applications of stochastic programming such as new results on risk modeling, on Monte Carlo sampling methods and approximations, and clarifies relationships to other methods. An extended chapter on stochastic integer programming reflects advances in this field. Naturally, much care is devoted to various aspects of solution methods.

The book is aimed at researchers, master’s level and postgraduate students of mathematics and also of related applied disciplines, such as operations research, finance, management, and engineering. With references to original papers, the authors include (mostly without proofs) mathematically advanced themes, e.g., properties of expectation functionals, optimality conditions, convergence results, for which knowledge of convex analysis and of optimization theory is expected. On the other hand, the worked examples and numerous exercises delineate clearly the wide-ranging possibilities of applications of stochastic programming and, at the same time, they help to build an intuition how to model uncertainty within mathematical programs and how to interpret the obtained results. The book will thus certainly attract also the wide spectrum of readers whose main interest lies in possible exploitation of stochastic programming methodology and will help them to find their own way to treat actual problems using stochastic programming methods.

As a whole, the three main building blocks of stochastic programming – stochastic modeling, optimization, numerical methods – are well represented and balanced.

Reviewer: Jitka Dupačová (Praha)