A version of the inexact Levenberg-Marquardt method for constrained nonsmooth equations

TL;DR

This paper introduces a new variant of the inexact Levenberg-Marquardt method tailored for constrained nonsmooth equations, emphasizing computational efficiency and convergence analysis under weaker assumptions.

Contribution

It proposes a local ILMM with feasible inexact projections and establishes its convergence and rate under semi-smoothness and weaker error bound conditions.

Findings

Convergence results for the proposed method are established.

The new scheme demonstrates computational advantages in experiments.

Abstract

We herein propose a variant of the projected inexact Levenberg--Marquardt method (ILMM) for solving constrained nonsmooth equations. Since the orthogonal projection onto the feasible set may be computationally expensive, we propose a local ILMM with feasible inexact projections. By using assumption of semi-smoothness and an error bound condition which is weaker than the standard full rank assumption, we establish its convergence results, including results on its rate. Finally, some computacional results are reported in order to illustrate the advantages of the new schemes.