An Implicit Extragradient Method for Hierarchical Variational Inequalities

作者：Yao, Yonghong^*; Liou, Yeong Cheng

来源：Fixed Point Theory and Applications, 2011, 2011(1): 697248.

DOI：10.1155/2011/697248

• KRASNOSELSKI-MANN ITERATION
• FIXED-POINT APPROACH
• NONEXPANSIVE-MAPPINGS
• MONOTONE MAPPINGS
• REGULARIZATION

As a well-known numerical method, the extragradient method solves numerically the variational inequality VI(C, A) of finding u is an element of C such that (Au, v-u) >= 0, for all v is an element of C. In this paper, we devote to solve the following hierarchical variational inequality HVI(C, A, f) Find (x) over tilde is an element of VI(C, A) such that <(I - f)(x) over tilde, x - (x) over tilde) >= 0, for all x is an element of VI(C, A). We first suggest and analyze an implicit extragradient method for solving the hierarchical variational inequality HVI(C, A, f). It is shown that the net defined by the suggested implicit extragradient method converges strongly to the unique solution of HVI (C, A, f) in Hilbert spaces. As a special case, we obtain the minimum norm solution of the variational inequality VI(C, A).

• 出版日期2011
• 单位天津工业大学