Title of Paper:EXTENDED LEVENBERG-MARQUARDT METHOD FOR COMPOSITE FUNCTION MINIMIZATION

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Date of Publication:2017-01-01

Journal:JOURNAL OF COMPUTATIONAL MATHEMATICS

Included Journals:SCIE

Volume:35

Issue:4

Page Number:529-546

ISSN No.:0254-9409

Key Words:Unconstrained minimization; Composite function; Levenberg-Marquardt method

Abstract:In this paper, we propose an extended Levenberg-Marquardt (ELM) framework that generalizes the classic Levenberg-Marquardt (LM) method to solve the unconstrained minimization problem min rho (r(x)), where r : R-n -> R-m and rho : Rm -> R We also develop a few inexact variants which generalize ELM to the cases where the inner subproblem is not solved exactly and the Jacobian is simplified, or perturbed. Global convergence and local superlinear convergence are established under certain suitable conditions. Numerical results show that our methods are promising.