Stochastic Decomposition: A Statistical Method for Large Scale Stochastic Linear Programming: 8 (Nonconvex Optimization and Its Applications, 8) - Hardcover

Higle, Julia L.; Sen, S.

Hardcover

ISBN 10: 0792338405 ISBN 13: 9780792338406

Publisher: Springer, 1996

Synopsis

Motivation Stochastic Linear Programming with recourse represents one of the more widely applicable models for incorporating uncertainty within in which the SLP optimization models. There are several arenas model is appropriate, and such models have found applications in air­ line yield management, capacity planning, electric power generation planning, financial planning, logistics, telecommunications network planning, and many more. In some of these applications, modelers represent uncertainty in terms of only a few seenarios and formulate a large scale linear program which is then solved using LP software. However, there are many applications, such as the telecommunications planning problem discussed in this book, where a handful of seenarios do not capture variability well enough to provide a reasonable model of the actual decision-making problem. Problems of this type easily exceed the capabilities of LP software by several orders of magnitude. Their solution requires the use of algorithmic methods that exploit the structure of the SLP model in a manner that will accommodate large scale applications.

About this title

Review

`... can be highly recommended to anyone who wants to understand what stochastic decomposition is all about ...'
Mathematical Reviews, 98d

Synopsis

This work summarizes developments related to a class of methods called Stochastic Decomposition (SD) algorithms, which represent an important shift in the design of optimization algorithms. Unlike traditional deterministic algorithms, SD combines sampling approaches from the statistical literature with traditional mathematical programming constructs (for example decomposition and cutting planes). This marriage of two highly computationally oriented disciplines leads to a line of work that is most definitely driven by computational considerations. Furthermore, the use of sampled data in SD makes it extremely flexible in its ability to accommodate various representations of uncertainty, including situations in which outcomes/scenarios can only be generated by an algorithm/simulation. The authors report computational results with some of the largest stochastic programs arising in applications. These results (mathematical as well as computational) are the "tip of the iceberg". Further research will uncover extensions of SD to a wider class of problems.

Edition details

• Publisher: Springer
• Publication date: 1996
• Language: English
• ISBN 10: 0792338405
• ISBN 13: 9780792338406
• Binding: Hardcover
• Number of pages: 246