In this paper, we propose two algorithms for solving nonlinear monotone operator equations. The two algorithms are based on the conjugate gradient method. The corresponding search directions were obtained via a modified memoryless symmetric rank-one (SR1) update. Independent of the line search, the two directions were shown to be sufficiently descent and bounded. Moreover, the convergence of the algorithms were established under suitable assumptions on the operator under consideration. In addition, numerical experiments were conducted on some benchmark test problems to depict the efficiency and competitiveness of the algorithms compared with existing algorithms. From the results of the experiments, we can conclude that the proposed algorithms are more efficient and robust.

在本文中，我们提出了两种求解非线性单调算子方程的算法。两种算法均基于共轭梯度法。相应的搜索方向是通过修改后的无记忆对称等级1（SR1）更新获得的。与线搜索无关，两个方向显示为足够下降并有界。而且，算法的收敛性是在考虑所考虑的算子的适当假设下建立的。此外，还对一些基准测试问题进行了数值实验，以说明该算法与现有算法相比的效率和竞争力。从实验的结果，我们可以得出结论，所提出的算法更加有效和健壮。