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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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 2 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1425305660

Digital Object Identifier
doi:10.1155/2014/497262

Mathematical Reviews number (MathSciNet)
MR3193624

Zentralblatt MATH identifier
07010657

Citation

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. https://projecteuclid.org/euclid.jam/1425305660


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