A stochastic approach to stability in stochastic programming

AbstractA random optimization problem P0 minx∈Г0(ω) ƒ0(x,ω), ω∈Ω, is approximated by a sequence of random surrogate problems (Pn)n∈N with Pn minx∈Гn(ω) ƒn(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