On stability in multiobjective programming — A stochastic approach

In this paper 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 behaviour of the constraint sets, the sets of efficient points and the solution sets if the size of 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, (ii) certain parameters have to be estimated.