A stochastic approach to stability in stochastic programming

Abstract

A random optimization problem P 0 min x∈Г 0(ω) ƒ 0(x,ω), ω∈Ω , is approximated by a sequence of random surrogate problems (P n) n∈ N with P n min x∈Г n(ω) ƒ n(x,ω), ω∈Ω ([Ω, Σ, P] a given probability space). We investigate the convergence almost surely and in probability of the optimal values and the solution sets. The results can be regarded as random versions of well-known stability statements of parametric programming. Semicontinuous convergence (almost surely, in probability) of sequences of random functions is a crucial assumption in this framework and will be investigated in more detail.