A SAMPLE AVERAGE APPROXIMATION METHOD BASED ON A GAP FUNCTION FOR STOCHASTIC MULTIOBJECTIVE OPTIMIZATION PROBLEMS

In this paper, we consider the sample average approximation method for stochastic multiobjective optimization problems without the scalarization parameters. By virtue of the gap function, we transform stochastic multiobjective optimization problems into stochastic optimization reformulation problems. Some properties of the reformulation problems are discussed. Then, we propose a sample average approximation method for solving the reformulation problems, and the convergence and the rates of convergence of optimal values and optimal solutions of the approximation problems are investigated. Furthermore, the rates of convergence of the weakly Pareto optimal for sample average approximation multiobjective problem are discussed under the error bound condition.