ASYMPTOTICS OF THE OPTIMAL VALUE OF SAA WITH AMIS ON MINIMAX STOCHASTIC PROGRAMS

The minimax stochastic programming problem is approximated in this paper using the sample average approximation with adaptive multiple importance sampling. We discuss the asymptotics and convergence of its optimal value. The core is the research and utilization of martingale difference sequences. The functional central limit theorem for martingale difference sequences is one of the main tools in studying the asymptotics. Finally, we apply this result to discuss a risk averse optimization problem.