Levenberg--Marquardt methods with strong local convergence properties for solving nonlinear equations with convex constraints
Two Levenberg-Marquardt algorithms are considered for the solution of a, not necessarily square, system of nonlinear equations with convex constraints. Motivated by an earlier paper of \textit{N. Yamashita} and \textit{M. Fukushima} [Comput. Suppl. 15, 239--249 (2001; Zbl 1001.65047)] the usual nonsingularity assumption is replaced by an error bound condition that allows the solution set to be (locally) nonunique. At each step, one of the algorithms solves a strictly convex minimization problem, while the other requires only the solution of one system of linear equations. Both methods are shown to converge locally quadratically. Some numerical examples for the second method are given.
scientific article; zbMATH DE number 2127102