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Research Article | Open Access

A modified BFGS quasi-Newton method with Wolfe line search for unconstrained optimization

Wen Zhang1( ), Tingting Guo1, Junfeng Wu2, Zhousheng Ruan1, Shufang Qiu1,3
School of Science, East China University of Technology, Nanchang 330013, China
School of Information and Artificial Intelligence, Nanchang Institute of Science and Technology, Nanchang 330108, China
School of Artificial Intelligence, Guangzhou Maritime University, Guangzhou 510725, China
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Abstract

In this article, we construct a modified BFGS quasi-Newton method with Wolfe line search to solve a nonlinear equations. Firstly, we propose a new quasi-Newton secant equation and the corresponding practical implementation algorithm by combining the classic BFGS with the strong Wolfe conditions. Furthermore, the local and superlinear rate of convergence of the modified quasi-Newton updates are derived theoretically. Lastly, numerical examples illustrate the effectiveness and stability of the proposed method.

Keywords

nonlinear equationsquasi-Newton methodBFGSWolfe line searchconvergence
CLC number: 49J35, 49M15, 49M37, 90C53

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AIMS Mathematics
Volume 11 Issue 1,
January 2026
Pages 767-784
DOI: 10.3934/math.2026033

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Cite this article:
Zhang W, Guo T, Wu J, et al. A modified BFGS quasi-Newton method with Wolfe line search for unconstrained optimization. AIMS Mathematics, 2026, 11(1): 767-784. https://doi.org/10.3934/math.2026033

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Received: 05 July 2025
Revised: 15 December 2025
Accepted: 06 January 2026
Published: 12 January 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)