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.
Citation: Wen Zhang, Tingting Guo, Junfeng Wu, Zhousheng Ruan, Shufang Qiu. A modified BFGS quasi-Newton method with Wolfe line search for unconstrained optimization[J]. AIMS Mathematics, 2026, 11(1): 767-784. doi: 10.3934/math.2026033
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.
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Wen Zhang, Tingting Guo, Junfeng Wu, Zhousheng Ruan, Shufang Qiu. A modified BFGS quasi-Newton method with Wolfe line search for unconstrained optimization[J]. AIMS Mathematics, 2026, 11(1): 767-784. doi: 10.3934/math.2026033
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