A nonsmooth Levenberg-Marquardt method for vertical complementarity problems

Abstract

A nonsmooth Levenberg-Marquard (LM) method with double parameter adjusting strategies is presented for solving vertical complementarity problems based on the computation of an element of a vextor-valued minimum function’s B-differential in this paper. At each iteration, the LM parameter is adjusted based on the norm of the vector-valued minimum function and the ratio between the actual reduction and the predicted reduction. Under the local error bound condition, which is strictly weaker than nonsingular assumption, the local convergence rate is discussed. Finally, the numerical tests indicate that the present algorithm is effective.