A new Levenberg-Marquardt type algorithm for solving nonsmooth constrained equations

We consider the problem of finding a solution of a nonsmooth constrained (not necessarily square) system of equations. Based upon the smoothing reformulation of the original problem, we present a Levenberg-Marquardt (L-M) type algorithm for solving nonsmooth constrained system of equations, which solves a linear system of equations at each iteration. This algorithm has global convergence property. Moreover, this algorithm is shown to converge locally quadratically under an error bound condition which is much weaker than the standard nonsingularity condition. Some numerical results for the presented method indicate that the algorithm works quite well in practice.