A new logarithmic-quadratic proximal method for nonlinear complementarity problems (Q732410)

The nonlinear complementarity problem can be formulated as finding the zero of an appropriately maximal monotone operator, which can be solved by the proximal point algorithm. In this paper a new logarithmic-quadratic proximal (LQP) method is proposed to solve nonlinear complementarity problems by using a new step size which can be obtained without the computation of the objective function. Each iteration contains a prediction and a correction. The predictor is obtained by solving the LQP system approximately under relaxed accuracy criterion. The global convergence of the proposed algorithm is established under some mild conditions. Two numerical examples are provided to illustrate the efficiency of the proposed algorithm.