A proximal point algorithm with asymmetric linear term

In this paper, we propose an asymmetric proximal point algorithm for solving variational inequality problems. The algorithm is “asymmetric” in the sense that the matrix in the linear proximal term is not necessary to be a symmetric matrix, which makes the method more flexible, especially in dealing with problems with separable structures. Under some suitable conditions, we prove the global linear convergence of the algorithm. To make the method more practical, we allow the subproblem to be solved in an approximate manner and a flexible inaccuracy criterion with constant parameter is adopted. Finally, we report some preliminary numerical results.

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