In this paper, a derivative-free Hestenes–Stielfel type method is proposed to solve large-scale nonlinear equations with convex constraints. The proposed method adopts the line search proposed by Ou and Li [J. Comput. Appl. Math. 56(1-2) (2018), pp. 195–216]. Unlike most existing methods, the global convergence of the proposed method is established under the assumption that the underlying mapping is Lipschitz continuous and satisfies a weaker monotonicity condition. Preliminary numerical experiments indicate that the proposed method is effective and promising. Furthermore, the proposed method is used to solve image restoration problem in compressive sensing.

在本文中，提出了一种无导数 Hestenes-Stielfel 类型的方法来求解具有凸约束的大规模非线性方程组。所提出的方法采用了欧和李提出的线搜索[J. 计算。应用程序。数学。56（1-2）（2018），第 195-216 页]。与大多数现有方法不同，所提出方法的全局收敛性是在假设基础映射是 Lipschitz 连续并满足较弱的单调性条件下建立的。初步的数值实验表明，所提出的方法是有效的和有前途的。此外，该方法用于解决压缩感知中的图像恢复问题。