Banach空间中关于变分不等式的收缩投影方法(英文)

Shrinking Projection Methods for Variational Inequalities in Banach Spaces?

在一致光滑的一致凸的Banach空间中,设计了一种收缩投影算法用以逼近变分不等式的解,并在紧算子减弱为连续算子的条件下,利用广义投影算子和K-K性质等技巧证明了该算法的强收敛性.所得结果是近期相关结果的改进与推广,其算法有重要应用.

In uniformly smooth and uniformly convex Banach spaces,a shrinking projection algorithm is proposed for finding an element of the solution set of variational inequalities,and a strong convergence theorem is proved by using the generalized projection operator,K-K property and other analysis techniques under the conditions of compact mappings weakening continuous mappings.The results of this paper improve and extend recent some relevant results.The proposed algorithm has important applications.