Stopping rules for a class of sampling-based stochastic programming algorithms

Operations Research

Volumn 46, Issue 5, 1998, Pages 710-718

  Morton, David P ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; MONTE CARLO METHODS; OPTIMIZATION; PROBLEM SOLVING; RANDOM PROCESSES; SAMPLING;

OPTIMAL OBJECTIVE FUNCTION; STOCHASTIC PROGRAMMING ALGORITHMS; STOPPING RULE THEORY; STOPPING RULES;

DYNAMIC PROGRAMMING;

EID: 0032155337     PISSN: 0030364X     EISSN: None     Source Type: Journal    
DOI: 10.1287/opre.46.5.710     Document Type: Article

References (16)

1. BEALE, E. M. L. 1955. On Minimizing a Convex Function Subject to Linear Inequalities. J. Royal Statistical Soc. 17B, 173-184.
2. BIRGE, J. R. 1985. Decomposition and Partitioning Methods for Multistage Stochastic Linear Programs. Opus. Res. 33, 989-1007.
3. BIRGE, J. R. AND R. J.-B. WETS. 1989. Sublinear Upper Bounds for Stochastic Programs with Recourse. Math. Programming 43, 131-149.
4. BIRGE, J. R. AND R. J.-B. WETS. 1986. Designing Approximation Schemes for Stochastic Optimization Problems, in particular, for Stochastic Programs with Recourse. Math. Programming Study 27, 54-102.
5. DANTZIG, G. B. 1955. Linear Programming Under Uncertainty. Mgmt. Sci. 1, 197-206.
6. DANTZIG, G. B. AND P. W. GLYNN. 1990. Parallel Processors for Planning Under Uncertainty. Ann. Opus. Res. 22, 1-21.
7. DANTZIG, G. B., P. W. GLYNN, M. AVRIEL, J. C. STONE, R. ENTRIKEN AND M. NAKAYAMA. 1989. Decomposition Techniques for Multi-Area Generation and Transmission Planning Under Uncertainty. EPRI Report 2940-1.
8. DUPAČOVÁ, J. AND R. J.-B. WETS. 1988. Asymptotic Behavior of Statistical Estimators and of Optimal Solutions of Stochastic Optimization Problems. Ann. Statistics 16, 1517-1549.
9. DWIGHT, H. B. 1958. Mathematical Tables of Elementary and Some Higher Mathematical Functions. Second Edition, Dover Publications Inc., New York, NY.
10. ERMOLIEV, Y. 1983. Stochastic Quasigradient Methods and their Applications to Systems Optimization. Stochastics 9, 1-36.
11. FELLER, W. 1957. An Introduction to Probability Theory and Its Applications, Volume I. Third Edition, John Wiley & Sons Inc., New York, NY.
12. FRAUENDORFER, K. 1988. Solving SLP Recourse Problems with Arbitrary Multivariate Distributions - The Dependent Case. Math. O. R. 13, 377-394.
13. GAIVORONSKI, A. 1988. Stochastic Quasigradient Methods and Their Implementation. In Numerical Techniques for Stochastic Optimization. Y. Ermoliev and R. J.-B. Wets (eds.), Springer Verlag, Berlin.
14. GASSMANN, H. I. 1989. Optimal Harvest of a Forest in the Presence of Uncertainty. Canadian J. Forest Res. 19, 1267-1274.
15. VAN SLYKE, R. M., R. J.-B. WETS. 1969. L-Shaped Linear Programs with Applications to Optimal Control and Stochastic Programming. SLAM J. Appl. Math. 17, 638-663.
16. WOLFRAM, S. 1988. Mathematica: A System for Doing Mathematics by Computer. Addison-Wesley Publishing Company, Redwood City, CA.