Regularization and Resolution of Monotone Variational Inequalities with Operators Given by Hypomonotone Approximations

We study the stability in reflexive, smooth and strictly convex Banach spaces of the classical Tikhonov-Browder operator regularization method for monotone variational inequalities with data perturbations. We prove that this regularization method is stable even if the perturbed data contain operators which fail to be monotone, but are strictly hypomonotone. We use this stability result in order to prove convergence in smooth uniformly convex spaces of an iterative algorithm for approximating solutions of monotone variational inequalities. The algorithm we analyze involves in computations the perturbed data only and it converges even if the perturbed operators are not necessarily monotone, but strictly hypomonotone.

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