ON THE LEVENBERG-MARQUARDT METHODS FOR CONVEX CONSTRAINED NONLINEAR EQUATIONS

摘要

In this paper, both the constrained Levenberg-Marquardt method and the projected Levenberg-Marquardt method are presented for nonlinear equations F(x) = 0 subject to x ∈ X, where X is a nonempty closed convex set. The Levenberg-Marquardt parameter is taken as ||.F(x_k)||_2~δ with δ ∈ (0,2]. Under the local error bound condition which is weaker than nonsingularity, the methods are shown to have the same convergence rate, which includes not only the convergence results obtained in [12] for 5 = 2 but also the results given in [7] for unconstrained nonlinear equations.