A generalized proximal-point-based prediction-correction method for variational inequality problems

Authors:
Deren Han
Affiliations:
School of Mathematics and Computer Sciences, Nanjing Normal University, Nanjing 210097, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

In a class of variational inequality problems arising frequently from applications, the underlying mappings have no explicit expression, which make the subproblems involved in most numerical methods for solving them difficult to implement. In this paper, we propose a generalized proximal-point-based prediction-correction method for solving such problems. At each iteration, we first find a prediction point, which only needs several function evaluations; then using the information from the prediction, we update the iteration. Under mild conditions, we prove the global convergence of the method. The preliminary numerical results illustrate the simplicity and effectiveness of the method.