Numerical Techniques for Stochastic Optimization / Edition 1

by Yuri Ermoliev, Roger J-B. Wets

Overview

Rapid changes in today's environment emphasize the need for models and methods capable of dealing with the uncertainty inherent in virtually all systems re­ lated to economics, meteorology, demography, ecology, etc. Systems involving interactions between man, nature and technology are subject to disturbances which may be unlike anything which has been experienced in the past. In the technological revolution increases uncertainty-as each new stage particular, perturbs existing knowledge of structures, limitations and constraints. At the same time, many systems are often too complex to allow for precise measure­ ment of the parameters or the state of the system. Uncertainty, nonstationarity, disequilibrium are pervasivE' characteristics of most modern systems. In order to manage such situations (or to survive in such an environment) we must develop systems which can facilitate oar response to uncertainty and changing conditions. In our individual behavior we often follow guidelines that are conditioned by the need to be prepared for all (likely) eventualities: insur­ ance, wearing seat·belts, savings versus investments, annual medical check.ups, even keeping an umbrella at the office, etc. One can identify two major types of mechanisms: the short term adaptive adjustments (defensive driving, mar­ keting, inventory control, etc.) that are made after making some observations of the system's parameters, and the long term anticipative actions (engineer­ ing design, policy setting, allocation of resources, investment strategies, etc.).

Product Details

ISBN-13:	9783642648137
Publisher:	Springer Berlin Heidelberg
Publication date:	10/04/2011
Series:	Springer Series in Computational Mathematics , #10
Edition description:	Softcover reprint of the original 1st ed. 1988
Pages:	571
Product dimensions:	5.98(w) x 9.02(h) x 0.05(d)

Table of Contents

I: Models, Motivation and Methods.- 1. Shastic Programming, an Introduction.- II: Numerical Procedures.- 2. Approximations in Shastic Programming.- 3. Large Scale Linear Programming Techniques.- 4. Nonlinear Programming Techniques Applied to Shastic Programs with Recourse.- 5. Numerical Solution of Probabilistic Constrained Programming Problems.- 6. Shastic Quasigradient Methods.- 7. Multidimensional Integration and Shastic Programming.- 8. Shastic Integer Programming.- III: Implementation.- 9. A Proposed Standard Input Format for Computer Codes which Solve Shastic Programs with Recourse.- 10. A Computer Code for Solution of Probabilistic constrained Shastic Programming Problems.- 11. Conditional Probability and Conditional Expectation of a Random Vector.- 12. An L-shaped Method Computer Code for Multistage Shastic Linear Programs.- 13. The Relationship Between the L-shaped Method and Dual Basis Factorization for Shastic Linear Programming.- 14. Design and Implementation of a Shastic Programming Optimizer with Recourse and Tenders.- 15. Finite Generation Method.- 16. Implementation of Shastic Quasigradient Methods.- 17. Stepsize Rules, Stopping Times and their Implementation in Shastic Quasigradient Algorithms.- 18. Adaptive Shastic Quasigradient Methods.- 19. A Note about Projections in the Implementation of Shastic Quasigradient Methods.- 20. Decent Shastic Quasigradient Methods.- 21. Shastic Integer Programming by Dynamic Programming.- IV: Applications and Test Problems.- 22. Facility Location Problem.- 23. Lake Entrophication Management: The Lake Balaton Project.- 24. Optimal Investments for Electricity Generation: A Shastic Model and a Test-Problem.- 25. Some Applications of Shastic Optimization Methods to the Electric Power System.- 26. Power Generation Planning with Uncertain Demand.- 27. Exhaustible Resource Models with Uncertain Returns from Exploration Investment.- 28. A Two-Stage Shastic Facility-Location Problem with Time-Dependent Supply.- 29. Some Test Problems for Shastic Nonlinear Multistage Programs.- 30. Shastic Programming Problems: Examples from the Literature.