A Modified Hestenes-Stiefel-Type Derivative-Free Method for Large-Scale Nonlinear Monotone Equations

Zhifeng Dai and Huan Zhu
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Zhifeng Dai: College of Mathematics and Computational Science, Changsha University of Science and Technology, Changsha 410114, China
Huan Zhu: College of Mathematics and Computational Science, Changsha University of Science and Technology, Changsha 410114, China

Mathematics, 2020, vol. 8, issue 2, 1-14

Abstract: The goal of this paper is to extend the modified Hestenes-Stiefel method to solve large-scale nonlinear monotone equations. The method is presented by combining the hyperplane projection method (Solodov, M.V.; Svaiter, B.F. A globally convergent inexact Newton method for systems of monotone equations, in: M. Fukushima, L. Qi (Eds.)Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, Kluwer Academic Publishers. 1998, 355-369) and the modified Hestenes-Stiefel method in Dai and Wen (Dai, Z.; Wen, F. Global convergence of a modified Hestenes-Stiefel nonlinear conjugate gradient method with Armijo line search. Numer Algor. 2012, 59, 79-93). In addition, we propose a new line search for the derivative-free method. Global convergence of the proposed method is established if the system of nonlinear equations are Lipschitz continuous and monotone. Preliminary numerical results are given to test the effectiveness of the proposed method.

Keywords: nonlinear equations; monotonicity property; projection method; global convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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