求解强单调变分不等式组新的自适应投影算法

A New Self-adaptive Projection Method for System of Strongly Monotone Variational Inequalities

自适应投影算法是求解强单调变分不等式的一种重要方法,在自然科学中的诸多领域有着广泛的应用.本文利用自适应投影算法来求解强单调变分不等式组,证明了这种算法的收敛性,本文结果将He B S,Yang H,Meng Q和Han D R改进的Goldstein-Levitin-Polyak投影算法运用到求解变分不等式组上,并构造出了简单实例证明所提出的算法的有效性和可操作性.

Self-adaptive projection algorithms are attractive methods solving strongly monotone variational inequalities.They can be applied to a large number of fileds of natural science.In this paper,we investigate a system of strongly monotone variational inequalities by using a self-adaptive projection method.We prove the convergence of this algorithm.The results presented in this paper use modified Goldstein-Levitin-Polyak projection method for a system of strongly monotone variational inequality problems,we also give simple examples to show the effectiveness and operability of the proposed algorithm.