In this paper, two effective derivative-free methods are proposed for solving large-scale nonlinear monotone equations, in which the search directions are sufficiently descent and independent of the line search. The methods are the extensions of the conjugate gradient methods proposed by Bojari and Eslahchi (Numer. Algorithms 83, pp. 901–933, 2020) combined with the hyperplane projection technique. Our approaches are low storage memory and derivative-free, which makes them suitable for large-scale nonsmooth monotone nonlinear equations. Under proper assumptions, we analyze the global convergence property of the proposed methods. Finally, numerical experiments show that the proposed methods outperform some existing ones.

本文提出了两种有效的无导数方法来求解大型非线性单调方程，其中搜索方向充分下降并且与线搜索无关。这些方法是Bojari和Eslahchi（Numer。算法83，第901–933页，2020）提出的共轭梯度方法与超平面投影技术的扩展。我们的方法是低存储内存和无导数的，这使其适用于大规模非光滑单调非线性方程。在适当的假设下，我们分析了所提出方法的全局收敛性。最后，数值实验表明，所提出的方法优于现有方法。