Right‐Hand Side Decomposition for Variational Inequalities

We consider a general class of variational inequality problems in a finite‐dimensional space setting. The cost mapping need not be the gradient of any function. By using a right‐hand side allocation technique, we transform such a problem into a collection of small‐dimensional variational inequalities. The master problem is a set‐valued variational inequality. We suggest a general iterative method for the problem obtained, which is convergent under monotonicity assumptions. We also show that regularization of partial problems enables us to create single‐valued approximations for the cost mapping of the master problem and to propose simpler solution methods.