An implementable nonlinear Lagrange algorithm for stochastic minimax problems is presented based on sample average approximation method in this paper, in which the second step minimizes a nonlinear Lagrange function with sample average approximation functions of original functions and the sample average approximation of the Lagrange multiplier is adopted. Under a set of mild assumptions, it is proven that the sequences of solution and multiplier obtained by the proposed algorithm converge to the Kuhn-Tucker pair of the original problem with probability one as the sample size increases. At last, the numerical experiments for five test examples are performed and the numerical results indicate that the algorithm is promising.
Suxiang He. Yunyun Nie. Xiaopeng Wang. "A Nonlinear Lagrange Algorithm for Stochastic Minimax Problems Based on Sample Average Approximation Method." J. Appl. Math. 2014 1 - 8, 2014. https://doi.org/10.1155/2014/497262