Stochastic optimization over a Pareto set associated with a stochastic multi-objective optimization problem
A problem of minimization of the expectation of a real random function is considered where the feasible region is a Pareto set of a stochastic optimization problem. The objectives of the latter are expectations of random functions. A method of the type of sample average approximation is developed. The almost sure convergence of the proposed method is proved in the case of strict convexity of the involved stochastic multi-objective problem. A similar result is proved also without a convexity assumption, however, in that case the convergence of the approximate solutions in the image space is considered. An illustrative example is included.
scientific article; zbMATH DE number 6363584
scientific article