文章针对实Hilbert空间中的单调变分不等式和不动点连续映射的凸可行性问题,提出了一种非单调步长算法来求解。该算法利用可行集的信息构造特殊半空间,以及结合外梯度方法构造半空间。每次向两个半空间作投影。同时结合惯性加速技巧与Mann迭代方法,在一定条件下,建立了所提算法的弱收敛性定理。最后,我们进行了一些计算测试,以证明所提算法的效率和优点,并与现有算法进行了比较。This paper presents a new inertial subgradient extragradient algorithm designed to solve variational inequalities and fixed point problems in real Hilbert spaces. Integrating the Mann iteration method with the subgradient extragradient approach and employing inertial acceleration techniques, the algorithm constructs a half-space using subgradient information and projects onto it. Step lengths are determined via a line search procedure, eliminating the need to compute the Lipschitz constant of the mapping. The algorithm’s weak convergence is established under assumptions like the pseudo-nonexpansiveness of the mappings. Finally, Numerical experiments additionally illustrate the algorithm’s advantages over existing approaches in the literature.
在灰色主成分分析方法的研究中,针对原有方法中用于主成分分析的关联度矩阵的伪相关性和波动型序列量化不准确的问题。在两方面进行改进,一是改进灰色相对关联度的取值范围,将其从0.5~1拓展到0~1;二是基于斜率思路引入了趋势概率关联度指标,度量序列在趋势变化方向上的表征。结合两种关联度,提出了可以替换相关系数或协方差矩阵的新关联度矩阵。模拟与实证结果显示,改进的灰色关联度矩阵能够更好的度量波动型序列特征,将其用于主成分分析聚类,可以发现更加丰富和合理的结果,与一般模型相比效果更优。In the research of the grey principal component analysis method, the issues of pseudo-correlation and inaccurate quantification of fluctuating sequences in the correlation matrix for principal component analysis were tackled. Two improvements were made in two respects. Firstly, the range of grey relative correlation was expanded from 0.5~1 to 0~1. Secondly, based on the slope concept, a trend probability correlation index was introduced to measure the representation of sequences in the trend change direction. By combining the two correlation indices, a new correlation matrix that can replace the correlation coefficient or covariance matrix was proposed. Simulation and empirical results indicate that the improved grey correlation matrix can better measure the features of fluctuating sequences and be used for principal component analysis clustering to yield more diverse and reasonable results, outperforming general models.
暂无评论