On the Glivenko-Cantelli Problem in Stochastic Programming: Linear Recourse and Extensions

References

• Artstein Z. , Wets R. J.-B. Stability results for stochastic programs and sensors, allowing for discontinuous objective functions. SIAM J. Optim. (1994) 4 537 550 Crossref, Google Scholar
• Attouch H. Variational Convergence for Functions and Operators (1984) (Pitman, Boston) Google Scholar
• Attouch H. , Wets R. J.-B. Epigraphical processes: Laws of large numbers for random lsc functions (1991) . Technical report, Department of Mathematics, University of California, Davis Google Scholar
• Bauer H. Wahrscheinlichkeitstheorie und Grundzüge der Maßtheorie (1974) (Walter de Gruyter, Berlin) . (English translation Probability Theory and Elements of Measure Theory, Academic Press, London, 1981) Google Scholar
• Dupačová J. , Wets R. J.-B. Asymptotic behavior of statistical estimators and of optimal solutions of stochastic optimization problems. Ann. Statist. (1988) 16 1517 1549 Crossref, Google Scholar
• Ermoliev Yu. M. , Norkin V. I. Normalized convergence in stochastic optimization. Ann. Oper. Res. (1991) 30 187 198 Crossref, Google Scholar
• Ermoliev Yu. M. , Wets R. J.-B. Numerical Techniques for Stochastic Optimization (1988) (Springer-Verlag, Berlin) Crossref, Google Scholar
• v.d. Geer S. A. , Stougie L. On rates of convergence and asymptotic normality in the multiknapsack problem. Math. Programming (1991) 51 349 358 Crossref, Google Scholar
• Giné E. , Zinn J. Some limit theorems for empirical processes. Ann. Probab. (1984) 12 837 870 Crossref, Google Scholar
• Kall P. , Guddat J. , Jongen H. , Kummer B. , Nožička F. On approximations and stability in stochastic programming. Parametric Optimization and Related Topics (1987) (Akademie-Verlag, Berlin) 387 407 Google Scholar
• Kall P. , Wallace S. W. Stochastic Programming (1994) (J. Wiley & Sons, Chichester) Google Scholar
• Kaniovski Yu. M. , King A. , Wets R. J.-B. Probabilistic bounds (via large deviations) for the solutions of stochastic programming problems. Ann. Oper. Res. (1995) 56 189 208 Crossref, Google Scholar
• King A. , Rockafellar R. T. Asymptotic theory for solutions in statistical estimation and stochastic programming. Math. Oper. Res. (1993) 18 148 162 Link, Google Scholar
• King A. , Wets R. J.-B. Epi-consistency of convex stochastic programs. Stochastics and Stochastic Rep. (1991) 34 83 92 Crossref, Google Scholar
• Luchetti R. , Salinetti G. , Wets R. J.-B. Uniform convergence of probability measures: Topological criteria. J. Multivar. Anal. (1994) 51 252 264 Crossref, Google Scholar
• Piersma N. Combinatorial optimization and empirical processes (1993) . Ph.D. dissertation, University of Amsterdam, Tinbergen Institute Research Series 52 Google Scholar
• Pollard D. Convergence of Stochastic Processes (1984) (Springer-Verlag, New York) Crossref, Google Scholar
• Ranga-Rao R. Relations between weak and uniform convergence of measures with applications. Ann. Math. Statist. (1962) 33 659 680 Crossref, Google Scholar
• Rhee W. T. , Talagrand M. A concentration inequality for the k-median problem. Math. Oper. Res. (1989) 14 189 202 Link, Google Scholar
• Robinson S. M. Local epi-continuity and local optimization. Math. Programming (1987) 37 208 222 Crossref, Google Scholar
• Robinson S. M. , Wets R. J.-B. Stability in two-stage stochastic programming. SIAM J. Control Optim. (1987) 25 1409 1416 Crossref, Google Scholar
• Römisch W. , Schultz R. Lipschitz stability for stochastic programs with complete recourse. SIAM J. Optim. (1997) . to appear Google Scholar
• Rubinstein R. Y. , Shapiro A. Discrete Event Systems: Sensitivity Analysis and Stochastic Optimization by the Score Function Method (1992) (John Wiley and Sons, New York) Google Scholar
• Schultz R. On structure and stability in stochastic programs with random technology matrix and complete integer recourse. Math. Programming (1995) 70 73 89 Crossref, Google Scholar
• Schultz R. Rates of convergence in stochastic programs with complete integer recourse. SIAM J. Optim. (1997) . to appear Google Scholar
• Shapiro A. Asymptotic properties of statistical estimators in stochastic programming. Ann. Statist. (1989) 17 841 858 Crossref, Google Scholar
• Shapiro A. Asymptotic behavior of optimal solutions in stochastic programming. Math. Oper. Res. (1993) 18 829 845 Link, Google Scholar
• Talagrand M. The Glivenko-Cantelli problem. Ann. Probab. (1987) 15 837 870 Crossref, Google Scholar
• Topsoe F. Uniformity in convergence of measures. Z. Wahrscheinlichkeitstheorie Werw. (1977) 39 1 30 Crossref, Google Scholar
• Vapnik V. N. , Červonenkis A. Y. Necessary and sufficient conditions for the uniform convergence of means to their expectations. Theory of Probab. Appl. (1981) 26 532 553 Crossref, Google Scholar
• Varadarajan V. S. On the convergence of sample probability distributions. Sankhya (1958) 19 23 26 Google Scholar
• Vogel S. On stability in multiobjective programming—A stochastic approach. Math. Programming (1992) 56 91 119 Crossref, Google Scholar
• Vogel S. A stochastic approach to stability in stochastic programming. J. Comput. Appl. Math. (1994) 56 65 96 Crossref, Google Scholar