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The new extragradient method extended to equilibrium problems

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

Malitsky and Semenov in (Cybern Syst Anal 50(2):271–277, 2014) introduced a new extragradient method for variational inequality problem. This paper extends the new extragradient method to equilibrium problems for pseudomonotone and Lipschitz-type continuous bifunctions. We have replaced naturally two projections in the new extragradient method by two optimization programs and proved the weak convergence of the proposed algorithm. The advantage of the algorithm is the computation of only one value of the bifunction in each iteration. In the numerical experiment, we see that the proposed algorithm has a competitive advantage over the time of execution and the iterative number.

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Acknowledgements

We greatly appreciate the referees for their really helpful and constructive comments. We also thank the National Natural Science Foundation of China(11401157) and the Key Laboratory of Machine Learning and Computational Intelligence of Hebei Province in College of Mathematics and Information Science of Hebei University for the support.

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  1. College of Mathematics and Information Science, Hebei University, Baoding, 071002, Hebei, China

    Ying Liu & Hang Kong

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  1. Ying Liu
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  2. Hang Kong
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Correspondence to Ying Liu.

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Liu, Y., Kong, H. The new extragradient method extended to equilibrium problems. RACSAM 113, 2113–2126 (2019). https://doi.org/10.1007/s13398-018-0604-y

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