An inexact derivative-free Levenberg-Marquardt method for linear inequality constrained nonlinear systems under local error bound conditions

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• 作者：Peng Wang^a ; ^{pengwang261@163.com" class="auth_mail" title="E-mail the corresponding author} ; ^{pengwang621@163.com" class="auth_mail" title="E-mail the corresponding author} ; Detong Zhu ; ^b ; ^{dtzhu@shnu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Derivative-free optimization ; Levenberg&ndash ; Marquardt method ; Inexact ; System of nonlinear equations ; Interior point ; Affine scaling
• 刊名：Applied Mathematics and Computation
• 出版年：2016
• 出版时间：5 May 2016
• 年：2016
• 卷：282
• 期：Complete
• 页码：32-52
• 全文大小：627 K

文摘

In this paper, a derivative-free affine scaling inexact Levenberg–Marquardt method with interior backtracking line search technique is considered for solving linear inequality constrained nonlinear systems. The proposed algorithm is designed to take advantage of the problem structure by building polynomial interpolation models for each function of nonlinear systems subject to the linear inequality constraints on variables. Each iterate switches to backtracking step generated by affine scaling inexact Levenberg–Marquardt method and satisfies strict interior point feasibility by line search backtracking technique. Under local error bounded assumption, the method is superlinear and quadratic convergent on F(x). The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.