THE PERTURBED TIKHONOV ALGORITHM AND SOME OF ITS APPLICATIONS

The proximal point algorithm has known these last years many developme nts connected wish the expansion of the variational convergence theory . Motivated by this fact and inspired by the work of A. Tikhonov and V . Arsenine in the context of convex optimization, we present a new alg orithm for searching a zero of a maximal monotone operator on a real H ilbert space. We study the perturbed version of this algorithm and est ablish a critical comparison with the perturbed proximal point algorit hm. We apply this new algorithm to convex optimization and to variatio nal inclusions or, more particularly, to variational inequalities.