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In this paper, we propose the modified prediction-correction methods for solving pseudomonotone variational inequalities problems. The proposed methods can be viewed as an extension of the method of He et al. [11, B.S. He and X.M. Yuan, Comparison of two kinds of prediction–correction methods for monotone variational inequalities, Computational Optimization and Applications, Vol. 27, pp. 247–267 (2004).] by additional projection step at each iteration under the relaxed condition where the mapping is pseudomonotone. The convergence of the proposed method is proved. The numerical results are given to verify the efficiency of the modified methods.

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