This paper proposes a modified scaled spectral-conjugate-based algorithm for finding solutions to monotone operator equations. The algorithm is a modification of the work of Li and Zheng in the sense that the uniformly monotone assumption on the operator is relaxed to just monotone. Furthermore, unlike the work of Li and Zheng, the search directions of the proposed algorithm are shown to be descent and bounded independent of the monotonicity assumption. Moreover, the global convergence is established under some appropriate assumptions. Finally, numerical examples on some test problems are provided to show the efficiency of the proposed algorithm compared to that of Li and Zheng.

中文翻译：

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求解单调算子方程的基于比例缩放谱共轭梯度的改进算法

本文提出了一种基于标度谱共轭的改进算法，用于寻找单调算子方程的解。该算法是对Li和Zheng的工作的改进，从某种意义上说，将算符上的统一单调假设简化为仅单调。此外，与Li和Zheng的工作不同，所提出算法的搜索方向显示出下降和有界，而与单调性假设无关。此外，全球融合是在某些适当的假设下建立的。最后，提供了一些测试问题的数值示例，以证明与Li和Zheng相比，该算法的效率。