In this paper, we present a new hybrid spectral-conjugate gradient (SCG) algorithm for finding approximate solutions to nonlinear monotone operator equations. The hybrid conjugate gradient parameter has the Polak–Ribière–Polyak (PRP), Dai-Yuan (DY), Hestenes-Stiefel (HS) and Fletcher-Reeves (FR) as special cases. Moreover, the spectral parameter is selected such that the search direction has the descent property. Also, the search directions are bounded and the sequence of iterates generated by the new hybrid algorithm converge globally. Furthermore, numerical experiments were conducted on some benchmark nonlinear monotone operator equations to assess the efficiency of the proposed algorithm. Finally, the algorithm is shown to have the ability to recover disturbed signals.

在本文中，我们提出了一种新的混合谱共轭梯度 (SCG) 算法，用于寻找非线性单调算子方程的近似解。混合共轭梯度参数有 Polak-Ribière-Polyak (PRP)、Dai-Yuan (DY)、Hestenes-Stiefel (HS) 和 Fletcher-Reeves (FR) 作为特殊情况。此外，选择谱参数使得搜索方向具有下降特性。此外，搜索方向是有界的，新混合算法生成的迭代序列全局收敛。此外，对一些基准非线性单调算子方程进行了数值实验，以评估所提出算法的效率。最后，该算法被证明具有恢复受干扰信号的能力。