A Relaxed Projection Method for Split Variational Inequalities
We study the recently introduced split variational inequality under the framework of variational inequalities in a product space. The feature of our equivalent formulation of split variational inequality is its variable separability (that is, splitting nature) together with a linear constraint. We propose a relaxed projection method, which fully exploits the splitting structure of split variational inequality and which is not only easily implementable, but also globally convergent under some mild conditions. Our numerical results on finding the minimum-norm solution of the split feasibility problem and on solving a separable and convex quadratic programming problem verify the efficiency and stability of our new method.
projection method split variational inequality split feasibility problem monotone operator separable structure 65k15 49j40 90c25 47j25