Epi‐consistency of convex stochastic programs

Abstract

This paper presents consistency results for sequences of optimal solutions to convex stochastic optimization problems constructed from empirical data, by applying the strong law of large numbers for random closed sets to the epigraphs of the conjugate functions. Because of the special properties of convexity and empirical measures, epi-consistency is obtained under very simple assumptions; nevertheless the results are broadly applicable to many situations arising in stochastic programming. A new epi-consistency result for stochastic linear programs with recourse is obtained