Hybrid methods for a class of monotone variational inequalities

作者：Lu Xiwen; Xu Hong Kun^*; Yin Ximing

来源：Nonlinear Analysis-Theory Methods & Applications, 2009, 71(3-4): 1032-1041.

DOI：10.1016/j.na.2008.11.067

• Hybrid method
• Variational inequality
• Nonexpansive mapping
• Iterative method
• Projection
• Hierarchical minimization

We use contractions to regularize a class of monotone variational inequalities, where the monotone operators are complements of nonexpansive mappings and the Solutions are sought in the set of fixed points of another nonexpansive mapping. Such variational inequalities include monotone inclusions and convex optimization problems to be solved over the fixed point sets of nonexpansive mappings. Both implicit and explicit schemes are shown to be strongly convergent. An application in hierarchical minimization is included.

• 出版日期2009-8-1
• 单位中山大学; 华东理工大学