Convergent cutting-plane and partial-sampling algorithm for multistage stochastic linear programs with recourse

Journal of Optimization Theory and Applications

Volumn 102, Issue 3, 1999, Pages 497-524

  Chen, Z L ^a   Powell, W B ^b  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

Convergence with probability one; Cutting planes; Multistage stochastic programming; Sampling

Indexed keywords

ITERATIVE METHODS; STOCHASTIC PROGRAMMING; STOCHASTIC SYSTEMS;

CONVERGENCE WITH PROBABILITY ONE; CUTTING PLANES; DIFFERENT STAGES; EXTREME POINTS; LINEAR PROGRAMS; MULTI-STAGE STOCHASTIC PROGRAMMING; MULTI-STAGES; RANDOM QUANTITY; SAMPLING ALGORITHM; STOCHASTICS;

LINEAR PROGRAMMING;

EID: 0033245908     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022641805263     Document Type: Article

References (24)

1. 1. POWELL, W. B., JAILLET, P., and ODONI, A., Stochastic and Dynamic Networks and Routing, Handbook in Operations Research and Management Science, Volume on Networks, Edited by C. Monma, T. Magnanti, and M. Ball, North Holland, Amsterdam, Holland, pp. 141-295, 1995.
2. 2. ESCUDERO, L. F., KAMESAM, P. V., KING, A. J., and WETS, R., Production Planning via Scenario Modeling, Annals of Operations Research, Vol. 43, pp. 311-335, 1993.
3. 3. MULVEY, J. M., and VLADIMIROU, H., Stochastic Network Programming for Financial Planning Problems, Management Science, Vol. 38, pp. 1642-1664, 1992.
4. 4. BIRGE, J. R., Stochastic Programming Computation and Applications, INFORMS Journal on Computing, Vol. 9, pp. 111-133, 1997.
5. 5. BIRGE, J. R., and MULVEY, J. M., Stochastic Programming in Industrial Engineering, Technical Report, Department of Industrial and Operations Engineering, University of Michigan, 1996.
6. 6. MULVEY, J. M., and RUSZCZYNSKI, A., A Diagonal Quadratic Approximation Method for Large-Scale Linear Programs, Operations Research Letters, Vol. 12, pp. 205-215, 1991.
7. 7. ROSA, C., and RUSZCZYNSKI, A., On Augmented Lagrangian Decomposition Methods for Multistage Stochastic Programs, Annals of Operations Research, Vol. 64, pp. 289-309, 1996.
8. 8. VAN SLYKE, R., and WETS, R., L-Shaped Linear Programs with Applications to Optimal Control and Stochastic Programming, SIAM Journal on Applied Mathematics, Vol. 17, pp. 638-663, 1969.
9. 9. BIRGE, J. R., Decomposition and Partitioning Techniques for Multistage Stochastic Linear Programs, Operations Research, Vol. 33, pp. 989-1007, 1985.
10. 10. ROCKAFELLAR, T. R., and WETS, R., Scenarios and Policy Aggregation in Optimization under Uncertainty, Mathematics of Operations Research, Vol. 16, pp. 119-147, 1991.
11. 11. GUPAL, A. M., and BAZHENOV, L. G., A Stochastic Method of Linearization, Cybernetics, Vol. 8, pp. 482-484, 1972.
12. 12. ERMOLIEV, Y., Stochastic Quasigradient Methods and Their Application to System Optimization, Stochastics, Vol. 9, pp. 1-36, 1983.
13. 13. CULIOLI, J. C., and COHEN, G., Decomposition/Coordination Algorithms in Stochastic Optimization, SIAM Journal on Control and Optimization, Vol. 28, pp. 1372-1403, 1990.
14. 14. HIGLE, J. L., and SEN, S., Stochastic Decomposition: An Algorithm for Two-Stage Linear Programs with Recourse, Mathematics of Operations Research, Vol. 16, pp. 650-669, 1991.
15. 15. ROBINSON, S. M., Analysis of Sample Path Optimization, Mathematics of Operations Research, Vol. 21, pp. 1-528, 1996.
16. 16. CHEUNG, R. K. M., and POWELL, W. B., A Stochastic Hybrid Approximation Procedure, with an Application to Dynamic Networks, Technical Report SOR-94-02, Department of Civil Engineering and Operations Research, Princeton University, 1994.
17. 17. WETS, R., Programming under Uncertainty: The Solution Set, SIAM Journal on Applied Mathematics, Vol. 14, pp. 1143-1151, 1966.
18. 18. WITTROCK, R. J., Advances in a Nested Decomposition Algorithm for Solving Staircase Linear Programs, Technical Report SOL-83-2, Stanford University, 1983.
19. 19. GASSMAN, H. I., MSLIP: A Computer Code for the Multistage Stochastic Linear Programming Problem, Mathematical Programming, Vol. 47, pp. 407-423, 1990.
20. 20. PEREIRA, M. V. F., and PINTO, L. M. V. G., Multistage Stochastic Optimization Applied to Energy Planning, Mathematical Programming, Vol. 52, pp. 359-375, 1991.
21. 21. INFANGER, G., Planning under Uncertainty: Solving Large-Scale Stochastic Linear Programs, Boyd and Fraser, Scientific Press Series, New York, New York, 1994.
22. 22. MORTON, D. P., An Enhanced Decomposition Algorithm for Multistage Stochastic Hydroelectric Scheduling, Annals of Operations Research, Vol. 64, pp. 211-235, 1996.
23. 23. INFANGER, G., and MORTON, D. P., Cut Sharing for Multistage Stochastic Linear Programs with Interstate Dependency, Mathematical Programming, Vol. 75, pp. 241-256, 1996.
24. 24. CHUNG, K. L., A Course in Probability Theory, Academic Press, New York, New York, 1974.