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Numerical Techniques for Stochastic Optimization

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Yuri Ermoliev
841 g
231x153x35 mm

I: Models, Motivation and Methods.- 1. Stochastic Programming, an Introduction.- II: Numerical Procedures.- 2. Approximations in Stochastic Programming.- 3. Large Scale Linear Programming Techniques.- 4. Nonlinear Programming Techniques Applied to Stochastic Programs with Recourse.- 5. Numerical Solution of Probabilistic Constrained Programming Problems.- 6. Stochastic Quasigradient Methods.- 7. Multidimensional Integration and Stochastic Programming.- 8. Stochastic Integer Programming.- III: Implementation.- 9. A Proposed Standard Input Format for Computer Codes which Solve Stochastic Programs with Recourse.- 10. A Computer Code for Solution of Probabilistic constrained Stochastic Programming Problems.- 11. Conditional Probability and Conditional Expectation of a Random Vector.- 12. An L-shaped Method Computer Code for Multistage Stochastic Linear Programs.- 13. The Relationship Between the L-shaped Method and Dual Basis Factorization for Stochastic Linear Programming.- 14. Design and Implementation of a Stochastic Programming Optimizer with Recourse and Tenders.- 15. Finite Generation Method.- 16. Implementation of Stochastic Quasigradient Methods.- 17. Stepsize Rules, Stopping Times and their Implementation in Stochastic Quasigradient Algorithms.- 18. Adaptive Stochastic Quasigradient Methods.- 19. A Note about Projections in the Implementation of Stochastic Quasigradient Methods.- 20. Decent Stochastic Quasigradient Methods.- 21. Stochastic 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 Stochastic Model and a Test-Problem.- 25. Some Applications of Stochastic 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 Stochastic Facility-Location Problem with Time-Dependent Supply.- 29. Some Test Problems for Stochastic Nonlinear Multistage Programs.- 30. Stochastic Programming Problems: Examples from the Literature.
Rapid changes in today's environment emphasize the need for models and meth­ ods 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, 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.).

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