A new filter-Levenberg-Marquardt method with disturbance for solving nonlinear complementarity problems (Q963957)

Recently, filter methods are extensively studied to handle nonlinear programming problems. Because of good numerical results, filter techniques have attached importance, too. The nonlinear complementarity problem can be reformulated as the least \(l_2\)-norm solution of an optimization problem. In this paper, basing on the ideas of smoothing Newton methods a new smoothing function with twice continuous differentiability is constructed to approximate the objective function in the problem. Combining the filter technique with this new smoothing function, the authors present a new filter Levenberg-Marquardt method to attack nonlinear complemetarity problems. Under the assumption that the level set of the problem is compact, the authors prove its global convergence.