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论文类型：期刊论文

发表时间：2017-01-01

发表刊物：JOURNAL OF COMPUTATIONAL MATHEMATICS

收录刊物：SCIE

卷号：35

期号：4

页面范围：529-546

ISSN号：0254-9409

关键字：Unconstrained minimization; Composite function; Levenberg-Marquardt method

摘要：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.