Nonconvex Optimization and Its Applications

A Statistical Method for Large Scale Stochastic Linear Programming

By: Julia L. Higle, S. Sen

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Hardcover | 29 February 1996

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248 Pages

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25.4 x 17.15 x 2.54

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This book 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 (e.g. decomposition, cutting planes etc.). 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.
Audience: Researchers in mathematical optimization, including those working in telecommunications, electric power generation, transportation planning, airlines and production systems. Also suitable as a text for an advanced course in stochastic optimization.

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

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You Can Find This Book In

Non-Fiction Mathematics Applied Mathematics Stochastics Optimisation Linear Programming Business & Management Operational Research Computing & I.T.Computer Programming & Software Development Probability & Statistics Engineering & Technology

Mechanical Engineering & Materials Production & Industrial Engineering Reference, Information & Interdisciplinary Subjects Research & Information Information theory Cybernetics & Systems Theory

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Paperback

Published: 22nd November 2013

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Preface
Acknowledgements
List of Algorithmic Statements
List of Figures
List of Tables
Two Stage Stochastic Linear Programs	p. 1
Sampling Within Stochastic Linear Programming	p. 35
Foundations of Stochastic Decomposition	p. 63
Stabilizing Stochastic Decomposition	p. 99
Stopping Rules for Stochastic Decomposition	p. 131
Guidelines for Computer Implementation	p. 165
Illustrative Computational Experiments	p. 185
Glossary	p. 215
Table of Contents provided by Blackwell. All Rights Reserved.

Nonconvex Optimization and Its Applications

A Statistical Method for Large Scale Stochastic Linear Programming

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

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