In this paper, a hybrid three-term conjugate gradient (CG) method is proposed to solve constrained nonlinear monotone operator equations. The search direction is computed such that it is close to the direction obtained by the memoryless Broyden–Fletcher–Goldferb–Shanno (BFGS) method. Without any condition, the search direction is sufficiently descent and bounded. Moreover, based on some conditions, the search direction satisfy the conjugacy condition without using any line search. The global convergence of the method is established under mild assumptions. Comparison with existing methods is done to test the efficiency of the proposed method through some numerical experiments. Lastly, the applicability of the proposed method is shown.

中文翻译：

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单调算子方程的混合BFGS类方法及其应用

本文提出了一种混合三项共轭梯度（CG）方法来求解约束非线性单调算子方程。计算搜索方向，使其接近无记忆 Broyden-Fletcher-Goldferb-Shanno (BFGS) 方法获得的方向。在没有任何条件的情况下，搜索方向是充分下降且有界的。而且，基于某些条件，搜索方向满足共轭条件，而不使用任何线搜索。该方法的全局收敛性是在温和的假设下建立的。通过数值实验与现有方法进行比较，以测试所提出方法的效率。最后，展示了所提出方法的适用性。