On the rate of convergence of optimal solutions of Monte Carlo approximations of stochastic programs

SIAM Journal on Optimization

Volumn 11, Issue 1, 2000, Pages 70-86

  Shapiro, Alexander ^a   Homem De Mello, Tito ^b  

^a Georgia Institute of Technology   (United States)

^b OHIO STATE UNIVERSITY   (United States)

Author keywords

Convex analysis; Large deviations theory; Monte Carlo simulation; Two stage stochastic programming with recourse

Indexed keywords

EID: 0034550507     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623498349541     Document Type: Article

References (21)

1. T.G. BAILEY, P.A. JENSEN, AND D.P. MORTON, Response surface analysis of two-stage stochastic linear programmmy with recourse, Naval Res. Logist., 46 (1999), pp. 753-776.
2. D.P. BERTSEKAS, Nonlinear Programming, Athena Scientific, Belmont, MA, 1995.
3. J.F. BONNANS AND A. SHAPIRO, Perturbation Analysis of Optimization Problems, Springer-Verlag, New York, 2000.
4. J.V. BURKE AND M.C. FERRIS, Weak sharp minima in mathematical programming, SIAM J. Control Optim., 31 (1993), pp. 1340-1359.
5. G.B. DANTZIG AND P.W. GLYNN, Parallel processors for planning under uncertainty, Ann. Oper. Res., 22 (1990), pp. 1-21.
6. H.A. DAVID, Order Statistics, 2nd ed., Wiley, New York, 1981.
7. A. DEMBO AND O. ZEITOUNI, Large Deviations Techniques and Applications, 2nd ed., Springer-Verlag, New York, 1998.
8. J.D. DEUSCHEL AND D.W. STROOCK, Large Deviations, Academic Press, Boston, 1989.
9. J. DUPAČOVÁ AND R.J.-B. WETS, Asymptotic behavior of statistical estimators and of optimal solutions of stochastic optimization problems, Ann. Statist., 16 (1988), pp. 1517-1549.
10. F. HIAI, Strong laws of large numbers for multivalued random variables, in Multifunctions and Integrands, A. Dold and B. Eckmann, eds., Springer-Verlag, Berlin, 1984.
11. J.L. HIGLE AND S. SEN, Finite master programs in regularized stochastic decomposition, Math. Programming, 67 (1994), pp. 143-168.
12. J.-B. HIRIART-URRUTY AND C. LEMARECHAL, Convex Analysis and Minimization Algorithms I, Springer-Verlag, Berlin, 1993.
13. Y.M. KANIOVSKI, A.J. KING, AND R.J.-B. WETS, Probabilistic bounds (via large deviations) for the solutions of stochastic programming problems, Ann. Oper. Res., 56 (1995), pp. 189-208.
14. A. J. KING AND ROGER J.-B. WETS, Epi-consistency of convex stochastic programs, Stochastics, 34 (1991), pp. 83-92.
15. A.J. KING AND R.T. ROCKAFELLAR, Asymptotic theory for solutions in statistical estimation and stochastic programming, Math. Oper. Res., 18 (1993), pp. 148-162.
16. G.CH. PFLUG, Stochastic programs and statistical data, Ann. Oper. Res., 85 (1999), pp. 59-78.
17. S.M. ROBINSON, Analysis of sample-path optimization, Math. Oper. Res., 21 (1996), pp. 513-528.
18. R.T. ROCKAFELLAR, Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
19. W. RÖMISCH AND R. SCHULTZ, Lipschitz stability for stochastic programs with complete recourse, SIAM J. Optim., 6 (1996), pp. 531-547.
20. A. SHAPIRO, Asymptotic behavior of optimal solutions in stochastic programming, Math. Oper. Res., 18 (1993), pp. 829-845.
21. A. SHAPIRO AND T. HOMEM-DE-MELLO, A simulation-based approach to stochastic programming with recourse, Math. Programming 81 (1998), pp. 301-325.