A modified combined relaxation method for non-linear convex variational inequalities

Abstract

We consider a class of non-linear problems which is intermediate between equilibrium and variational inequality ones and has many applications. Unlike the usual variational inequality it involves two non-linear mappings, which need not be differentiable. We propose a class of iterative methods for this problem, which converge to a solution under weakened monotonicity type assumptions. This method is simpler essentially in comparison with those for the corresponding non-linear equilibrium problems.

Keywords:

• non-linear variational inequality
• non-differentiable mappings
• combined relaxation method
• equilibrium problems
• weakened monotonicity

AMS Subject Classifications:

• 90C33
• 65K10
• 47J20

Acknowledgments

This work was supported by the RFBR grant, project No. 13-01-00368a.