Solving the affine variational inequalities problem using optimization techniques

Abstract

This thesis concerns the resolution of the affine variational inequalities problem. For the monotone case, we used an interior-point method based on the algebraic transformation technique. For the non-monotone case, we proposed a DC method via its associated quadratic problem passing through the optimality condition. We carried out a theoretical and algorithmic study for the two methods and shown the convergence of each algorithm corresponding to its approach. We also gave the algorithmic complexity rate of the first method. The results obtained have been consolidated by very significant digital experiments.