A new Filter-Levenberg–Marquardt method with disturbance for solving nonlinear complementarity problems

Abstract

Recently, filter methods are extensively studied to handle nonlinear programming problems. Because of good numerical results, filter techniques are attached importance to. The nonlinear complementarity problem can be reformulated as the least l 2 -norm solution of an optimization problem. In this paper, basing on the filter technique and the new smoothing function, we present a new Filter-Levenberg–Marquardt method for solving the equation system Ψ ( z k ) + [ M ( z k ) + λ k I ] Δ z k = β k z ¯ with the disturbance β k z ¯ . Under the assumption that the lever set of the problem is compact, we prove its global convergence.