On stability in multiobjective programming - a stochastic approach

We assume that a deterministic multiobjective programming problem is approximated by surrogate problems based on estimations for the objective functions and the constraints. Making use of a large deviations approach, we investigate the behavior of the constraint sets, the sets of efficient points and the solution sets if the underlying sample tends to infinity. The results are illustrated by applying them to stochastic programming with chance constraints where (i) the distribution function of the random variable is estimated by the empirical distribution function and (ii) certain parameters are estimated.