Strong convergence of an inexact projected subgradient method for mixed variational inequalities

Abstract

In this article, we propose an easily implementable algorithm method for solving mixed variational inequalities. The proposed method combines two strategies: inexact projected subgradient methods and regularization techniques. We prove that the sequence generated by the method is strongly convergent to a solution of the problem in Hilbert spaces, whenever it exists. The results presented in this article generalize and improve some recent results.

Keywords:

• mixed variational inequality
• inexact projected subgradient method
• strong convergence

AMS Subject Classifications::

• 49J40
• 47J20

Acknowledgements

The authors are grateful to the editor and the referee for their valuable comments and suggestions. This work was supported by the Key Program of NSFC (Grant No. 70831005), the National Natural Science Foundation of China (11171237, 11101069) and the Fundamental Research Funds for the Central Universities (Grant No. 2009SCU11096).