Some proximal algorithms for linearly constrained general variational inequalities

Abstract

Based on the classical proximal point algorithm (PPA), some PPA-based numerical algorithms for general variational inequalities (GVIs) have been developed recently. Inspired by these algorithms, in this article we propose some proximal algorithms for solving linearly constrained GVIs (LCGVIs). The resulted subproblems are regularized proximally, and they are allowed to be solved either exactly or approximately.

Keywords:

• general variational inequality
• linear constraint
• proximal point algorithm
• inexact methods

AMS Subject Classifications::

• 90C25
• 90C30
• 65K10

Acknowledgements

M. Li was supported by Social Sciences Foundation by the State Education Commission 09YJA630020, the NSFC grant 10926147 and 11001053. X.M. Yuan was supported in part by FRG/08-09/II-40 from Hong Kong Baptist University and the NSFC grant 10701055.