Enhanced algorithms for stochastic programming
- Stanford Univ., CA (United States)
In this dissertation, we present some of the recent advances made in solving two-stage stochastic linear programming problems of large size and complexity. Decomposition and sampling are two fundamental components of techniques to solve stochastic optimization problems. We describe improvements to the current techniques in both these areas. We studied different ways of using importance sampling techniques in the context of Stochastic programming, by varying the choice of approximation functions used in this method. We have concluded that approximating the recourse function by a computationally inexpensive piecewise-linear function is highly efficient. This reduced the problem from finding the mean of a computationally expensive functions to finding that of a computationally inexpensive function. Then we implemented various variance reduction techniques to estimate the mean of a piecewise-linear function. This method achieved similar variance reductions in orders of magnitude less time than, when we directly applied variance-reduction techniques directly on the given problem. In solving a stochastic linear program, the expected value problem is usually solved before a stochastic solution and also to speed-up the algorithm by making use of the information obtained from the solution of the expected value problem. We have devised a new decomposition scheme to improve the convergence of this algorithm.
- Research Organization:
- Stanford Univ., CA (United States). Systems Optimization Lab.
- Sponsoring Organization:
- USDOE; National Science Foundation (NSF); Electric Power Research Inst.
- DOE Contract Number:
- FG03-92ER25116
- OSTI ID:
- 10139475
- Report Number(s):
- SOL-93-8; ON: DE94009423; BR: KC0701010; CNN: ECS-8906260; RP8010-09
- Resource Relation:
- Other Information: TH: Thesis (Ph.D.); PBD: Sep 1993
- Country of Publication:
- United States
- Language:
- English
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