The Perturbed Tikhonov's Algorithm and Some of its Applications

The proximal point algorithm has known these last years many developments connected with the expansion of the variational convergence theory. Motivated by this fact and inspired by the work of A. Tikhonov and V. Arsénine in the context of convex optimization, we present a new algorithm for searching a zero of a maximal monotone operator on a real Hilbert space. We study the perturbed version of this algorithm and establish a critical comparison with the perturbed proximal point algorithm. We apply this new algorithm to convex optimization and to variational inclusions or, more particularly, to variational inequalities.