In this paper, a new conjugate gradient-based projection method for solving a system of nonlinear monotone equations is proposed. The method can be viewed as an extension of a family of conjugate gradient methods for unconstrained optimization by Li et al. [16]. The proposed method is derivative-free which makes it suitable for large-scale nonlinear monotone equations. We show that the method satisfies the descent condition independent of line searches and that the method is globally convergent. Numerical results indicate that the proposed method is efficient.

中文翻译：

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非线性单调方程组的全局收敛投影方法

本文提出了一种新的基于共轭梯度的投影方法来求解非线性单调方程组。Li等人可以将该方法视为共轭梯度方法系列的扩展，以实现无约束优化。[16]。该方法无导数，适用于大规模非线性单调方程。我们表明该方法满足下降条件，与线搜索无关，并且该方法是全局收敛的。数值结果表明，该方法是有效的。