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An ε-generalized gradient projection method for nonlinear minimax problems

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Abstract

In this paper, combining the techniques of ε-generalized gradient projection and Armjio’s line search, we present a new algorithm for the nonlinear minimax problems. At each iteration, the improved search direction is generated by an ε-generalized gradient projection explicit formula. Under some mild assumptions, the algorithm possesses global and strong convergence. Finally, some preliminary numerical results show that the proposed algorithm performs efficiently.

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Acknowledgements

The author wishes to thank the reviewers for their constructive and pertinent suggestions for improving the presentation of the work. This work is supported by the National Natural Science Foundation of China (Grant Nos. 11271086, 11171250), the Guangxi Natural Science Foundation of China (Grant Nos. 2011GXNSFD018002, 2013GXNSFAA019009), the Youth Foundation of Yulin Normal University (Grant No. 2011YJQN03), and Innovation Group of Talents Highland of Guang Xi Higher School.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, P.R. China

    Guo-Dong Ma

  2. School of Mathematics and Information Science, Yulin Normal University, Yulin, Guangxi, 537000, P.R. China

    Guo-Dong Ma & Jin-Bao Jian

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  1. Guo-Dong Ma
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  2. Jin-Bao Jian
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Correspondence to Jin-Bao Jian.

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Ma, GD., Jian, JB. An ε-generalized gradient projection method for nonlinear minimax problems. Nonlinear Dyn 75, 693–700 (2014). https://doi.org/10.1007/s11071-013-1095-1

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  • DOI: https://doi.org/10.1007/s11071-013-1095-1

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