BookDOI
Introduction to Stochastic Programming
John R. Birge,Franois Louveaux +1 more
- Iss: 1
Reads0
Chats0
TLDR
This textbook provides a first course in stochastic programming suitable for students with a basic knowledge of linear programming, elementary analysis, and probability to help students develop an intuition on how to model uncertainty into mathematical problems.Abstract:
The aim of stochastic programming is to find optimal decisions in problems which involve uncertain data. This field is currently developing rapidly with contributions from many disciplines including operations research, mathematics, and probability. At the same time, it is now being applied in a wide variety of subjects ranging from agriculture to financial planning and from industrial engineering to computer networks. This textbook provides a first course in stochastic programming suitable for students with a basic knowledge of linear programming, elementary analysis, and probability. The authors aim to present a broad overview of the main themes and methods of the subject. Its prime goal is to help students develop an intuition on how to model uncertainty into mathematical problems, what uncertainty changes bring to the decision process, and what techniques help to manage uncertainty in solving the problems.In this extensively updated new edition there is more material on methods and examples including several new approaches for discrete variables, new results on risk measures in modeling and Monte Carlo sampling methods, a new chapter on relationships to other methods including approximate dynamic programming, robust optimization and online methods.The book is highly illustrated with chapter summaries and many examples and exercises. Students, researchers and practitioners in operations research and the optimization area will find it particularly of interest. Review of First Edition:"The discussion on modeling issues, the large number of examples used to illustrate the material, and the breadth of the coverage make'Introduction to Stochastic Programming' an ideal textbook for the area." (Interfaces, 1998)read more
Citations
More filters
Journal ArticleDOI
Conditional value-at-risk for general loss distributions
TL;DR: Fundamental properties of conditional value-at-risk are derived for loss distributions in finance that can involve discreetness and provides optimization shortcuts which, through linear programming techniques, make practical many large-scale calculations that could otherwise be out of reach.
Book
Lectures on Stochastic Programming: Modeling and Theory
TL;DR: The authors dedicate this book to Julia, Benjamin, Daniel, Natan and Yael; to Tsonka, Konstatin and Marek; and to the Memory of Feliks, Maria, and Dentcho.
Journal ArticleDOI
Theory and Applications of Robust Optimization
TL;DR: This paper surveys the primary research, both theoretical and applied, in the area of robust optimization (RO), focusing on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of the methodology.
Journal ArticleDOI
Robust solutions of uncertain linear programs
Aharon Ben-Tal,Arkadi Nemirovski +1 more
TL;DR: It is shown that the RC of an LP with ellipsoidal uncertainty set is computationally tractable, since it leads to a conic quadratic program, which can be solved in polynomial time.
Journal ArticleDOI
The Sample Average Approximation Method for Stochastic Discrete Optimization
TL;DR: A Monte Carlo simulation--based approach to stochastic discrete optimization problems, where a random sample is generated and the expected value function is approximated by the corresponding sample average function.