Improved convergence results for a modified Levenberg-Marquardt method for nonlinear equations and applications in MPCC

摘要

In this paper, we first consider a modified Levenberg-Marquardt method for solving nonlinear equations and show that the method converges superlinearly to a solution of the nonlinear equations under suitable conditions. Then, we reformulate the C-/M-/S-stationarity conditions of mathematical program with complementarity constraints as nonlinear equations so that we may employ the modified Levenberg-Marquardt method to solve these stationarity systems. Preliminary numerical experiments show that the new approach is promising.