Journal of Applied Mathematics

A Nonlinear Lagrange Algorithm for Stochastic Minimax Problems Based on Sample Average Approximation Method

Suxiang He, Yunyun Nie, and Xiaopeng Wang

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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.

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J. Appl. Math., Volume 2014 (2014), Article ID 497262, 8 pages.

First available in Project Euclid: 2 March 2015

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He, Suxiang; Nie, Yunyun; Wang, Xiaopeng. A Nonlinear Lagrange Algorithm for Stochastic Minimax Problems Based on Sample Average Approximation Method. J. Appl. Math. 2014 (2014), Article ID 497262, 8 pages. doi:10.1155/2014/497262.

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