In this paper, a derivative-free $RMIL$ conjugate gradient projection method for solving large-scale nonlinear monotone equations with convex constraints is proposed. The proposed method is a modification of an $RMIL$ conjugate gradient method combined with the projection techniques. We establish its global convergence under appropriate conditions. The method is then compared with other existing methods in the literature and the numerical results indicate that the method is efficient. Furthermore, the proposed method is used to recover a sparse signal from an incomplete and contaminated sampling measurements and the results are promising.

中文翻译：

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凸约束非线性单调方程的无导数RMIL共轭梯度投影方法及其在压缩传感中的应用

本文无导数 $\mathrm{[R}\mathrm{中号}\mathrm{一世}\mathrm{大号}$提出了一种共轭梯度投影方法，求解具有凸约束的大型非线性单调方程。提出的方法是对$\mathrm{[R}\mathrm{中号}\mathrm{一世}\mathrm{大号}$共轭梯度法与投影技术相结合。我们在适当的条件下建立其全球融合。然后将该方法与文献中其他现有方法进行比较，数值结果表明该方法是有效的。此外，所提出的方法被用于从不完整和被污染的采样测量中恢复稀疏信号，并且结果是有希望的。