改进的用于求解变分不等式的邻近点分裂算法(英文)

A MODIFIED PROXIMAL-BASED DECOMPOSITION METHOD FOR VARIATIONAL INEQUALITIES

本文在Chen和Teboulle于1994年提出的邻近点分裂算法的基础上提出了两类求解变分不等式的预测-校正算法,并且证明了在一定条件下,两类算法均具有全局收敛性.从理论上证明了,第二类算法每次迭代所产生的新的迭代点与解点的距离的下界大于第一类算法,从而说明了第二类算法优于第一类算法.

Based on the proximal-based decomposition （PBD） method proposed by Chen and Teboulle [Math. Progr. 64（1994）, pp.81-101], in this paper we propose two prediction-correction methods for solving variational inequalities. Under certain conditions, the global convergence of both methods is proved. It is proved theoretically that the lower-bound of the progress obtained by the second method is greater than that by the first one.