Efficient implementation of a modified and relaxed hybrid steepest-descent method for a type of variational inequality

Journal of inequalities and applications

Haiwen Xu¹ 

关键词: hybrid steepest-descent method;    variational inequalities;    approximate projection contraction method;    strong convergence;    nonexpansive mapping;   

DOI  :  10.1186/1029-242X-2012-93

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

To reduce the difficulty and complexity in computing the projection from a real Hilbert space onto a nonempty closed convex subset, researchers have provided a hybrid steepest-descent method for solving VI(F, K) and a subsequent three-step relaxed version of this method. In a previous study, the latter was used to develop a modified and relaxed hybrid steepest-descent (MRHSD) method. However, choosing an efficient and implementable nonexpansive mapping is still a difficult problem. We first establish the strong convergence of the MRHSD method for variational inequalities under different conditions that simplify the proof, which differs from previous studies. Second, we design an efficient implementation of the MRHSD method for a type of variational inequality problem based on the approximate projection contraction method. Finally, we design a set of practical numerical experiments. The results demonstrate that this is an efficient implementation of the MRHSD method.

【 授权许可】

CC BY