Convergence analysis of stochastic algorithms

Mathematics of Operations Research

Volumn 21, Issue 3, 1996, Pages 615-628

  Shapiro, A ^a   Wardi, Y ^b  

^a Georgia Institute of Technology   (United States)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Convex analysis; Gradient descent methods; Nondifferentiable optimization; Stochastic optimization; Uniform laws of large numbers

Indexed keywords

ALGORITHMS; ASYMPTOTIC STABILITY; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; DISCRETE TIME CONTROL SYSTEMS; ITERATIVE METHODS; MATHEMATICAL MODELS; MONTE CARLO METHODS; NONLINEAR PROGRAMMING; OPTIMIZATION; RANDOM PROCESSES;

ASYMPTOTIC CONVERGENCE; CONVERGENCE ANALYSIS; DISCRETE EVENT DYNAMIC SYSTEM MODELS; STOCHASTIC ALGORITHMS;

NUMERICAL ANALYSIS;

EID: 0030204613     PISSN: 0364765X     EISSN: None     Source Type: Journal    
DOI: 10.1287/moor.21.3.615     Document Type: Article

References (25)

1. Armijo, L. (1966). Minimization of functions having continuous partial derivatives. Pacific J. Math. 16 1-3.
2. Clarke, F. H. (1983). Optimization and Nonsmooth Analysis, Wiley, New York.
3. Dem'yaov, V. F., L. V. Vasil'ev (1985). Nondifferentiable Optimization, Optimization Software, New York.
4. Dupuis, P., R. Simha (1991). On sampling controlled stochastic approximation. IEEE Trans. Automat. Control AC-36 915-924.
5. Fu, M. C. (1994). Optimization via simulation: A review. Ann. Oper. Res. 53 199-247.
6. Hiriart-Urruty, J. B., C. Lemaréchal (1993a). Convex Analysis and Minimization Algorithms. I. Springer-Verlag, Berlin.
7. _, _ (1993b). Convex Analysis and Minimization Algorithms. II, Springer-Verlag, Berlin.
8. Ho, Y. C., X. R. Cao (1991). Perturbation Analysis of Discrete Event Dynamic Systems, Kluwer Academic Publishers, Boston, MA.
9. Kushner, H. J., D. S. Clark (1978). Stochastic Approximation Methods for Constrained and Unconstrained Systems, Springer-Verlag, New York.
10. Luenberger, D. G. (1989). Linear and Nonlinear Programming, Addison-Wesley Publishing Company, Second Edition, London.
11. Meheshwari, S., H. Mukai (1986). An optimization algorithm driven by probabilistic simulation. Proc. Conference on Decision and Control, Athens, Greece, 1703-1705.
12. Mukai, H., D. Yan (1991). Methods for minimizing the expectation. Presented at the NSF Workshop on Discrete Event Dynamic Systems, Amherst, MA.
13. Plambeck, E. L., B. R. Fu, S. M. Robinson, R. Suri (1995). Optimizing performance functions in stochastic systems. Math. Programming (to appear).
14. Polak, E. (1987). On the mathematical foundations of nondifferentiable optimization in engineering design. SIAM Rev. 29 21-89.
15. Robinson, S. M. (1995). Convergence of subdifferentials under strong stochastic convexity. Management Sci. 41 1397-1401.
16. Rockafellar, R. T. (1970). Convex Analysis, Princeton University Press, NJ.
17. Rubinstein, R. Y., A. Shapiro (1993). Discrete Event Systems: Sensitivity Analysis and Stochastic Optimization by the Score Function Method. John Wiley and Sons, New York.
18. Shapiro, A. (1989). Asymptotic properties of statistical estimators in stochastic programming. Ann. Statist. 17 841-858.
19. _, Y. Wardi (1994). Nondifferentiability of the steady state function in discrete event dynamic systems. IEEE Trans. Automat. Control 39 1707-1711.
20. Simha, R., J. F. Kurose (1989). Stochastic approximation schemes for a load balancing problem. Proc. 27th Annual Allerton Conf., Allerton, IL.
21. Wardi, Y. (1990). Stochastic algorithms with Armijo step sizes for minimization of functions. J. Optim. Theory Appl. 64 399-417.
22. _, K. Lee (1991). Application of descent algorithms with Armijo stepsizes to simulation-based optimization of queueing networks. Proc. 30th Conf. on Decision and Control, Brighton, England, 110-115.
23. _, M. W. McKinnon, R. Schuckle (1991). On perturbation analysis of queueing networks with finitely supported service time distributions. IEEE Trans. Automat. Control AC-36 863-867.
24. Yan, D., H. Mukai (1995). An optimization algorithm with probabilistic simulation. J. Optim. Theory Appl. (to appear).
25. Zangwill, W. J. (1967). Nonlinear Programming, A Unified Approach, Prentice-Hall, NJ.