A locally convergent inexact projected Levenberg–Marquardt-type algorithm for large-scale constrained nonsmooth equations

Abstract

This work presents a variant of an inexact projected Levenberg–Marquardt algorithm for solving constrained nonsmooth equations. More precisely, we propose a local inexact Levenberg–Marquardt algorithm with feasible inexact projection, since the orthogonal projection onto the feasible set may be computationally expensive. Under the assumption of semismoothness and an error bound condition, the local convergence as well as results on the convergence rate of the proposed algorithm are established. Finally, some computational results are reported to illustrate the advantages of the new schemes.