数值结果显示了该方法的优越性，包括迭代序列的单调收敛性及有限差分解的高精度。
The numerical results demonstrate the advantages of the method, including the monotone convergence property of iterative sequences and the high accuracy of the method.
提出一个新的下降方向，在函数伪单调的条件下证明了算法的全局收敛性。
In this paper, we propose a new descent direction. Under the pseudomonotone of the underlying function, we prove the global convergence of the algorithm.
本文研究了系数为强单调算子的椭圆型偏微分方程，得到了解的梯度的几乎处处收敛性。
In this paper, we study the elliptic partial differential Cquation whose coefficients are strongly monotony operators, and obtain the everywhere convergence of the gradients of solutions.
本文提出一类求解无约束优化问题的非单调曲线搜索方法，在较弱条件下证明了其收敛性。
This paper presents a non-monotone curve search method for unconstrained optimization problems and proves its convergence under some mild conditions.
本文主要运用一种具有全局收敛性的单调迭代法求解了一类非线性扩散方程的数值解。
This paper mainly studies the numerical solution of a class of nonlinear diffusion equations using a monotone iteration method with the global convergence.
为改进网络学习效率及大范围收敛性，提出了网络权值学习的单调同伦方法，该方法具有与牛顿法相同的二阶收敛性。
To improve the learning efficiency and global convergence we present the monotone homotopy method, which has the same convergence as the Newton's method, to train the weights of the network.
给出一种新的非单调信赖域方法，证明了算法的全局收敛性和超线性收敛性，最后给出了数值结果。
A new nonmonotonic trust region method is given in this paper. And its global convergence and superlinear convergence are proved. Numerical results are given.
给出求解单调变分不等式问题的一个近似邻近点算法，在不需要任何中间步骤的条件下证明算法的收敛性。
This paper presents a approximate proximal algorithm finding the zero of a maximal monotone operator in Hilbert space, whose error criterion is weaker than that in the literatures.
给出求解单调变分不等式问题的一个近似邻近点算法，在不需要任何中间步骤的条件下证明算法的收敛性。
This paper presents a approximate proximal algorithm finding the zero of a maximal monotone operator in Hilbert space, whose error criterion is weaker than that in the literatures.
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