Next Article in Journal
Prediction of Extracellular Matrix Proteins by Fusing Multiple Feature Information, Elastic Net, and Random Forest Algorithm
Previous Article in Journal
Diffeological Statistical Models, the Fisher Metric and Probabilistic Mappings
Open AccessArticle

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

College of Mathematics and Computational Science, Changsha University of Science and Technology, Changsha 410114, China
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(2), 168; https://doi.org/10.3390/math8020168
Received: 26 December 2019 / Revised: 16 January 2020 / Accepted: 21 January 2020 / Published: 30 January 2020
(This article belongs to the Special Issue Iterative Methods for Solving Nonlinear Equations and Systems 2020)
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. View Full-Text
Keywords: nonlinear equations; monotonicity property; projection method; global convergence nonlinear equations; monotonicity property; projection method; global convergence
MDPI and ACS Style

Dai, Z.; Zhu, H. A Modified Hestenes-Stiefel-Type Derivative-Free Method for Large-Scale Nonlinear Monotone Equations. Mathematics 2020, 8, 168.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop