THE PERTURBED GENERALIZED TIKHONOV’S ALGORITHM

Abstract. We work on the research of a zero of a maximal monotone operator on a real Hilbert space. Following the recent progress made in the context of the proximal point algorithm devoted to this problem, we introduce simultaneously a variable metric and a kind of relaxation in the perturbed Tikhonov’s algorithm studied by P. Tossings. So, we are led to work in the context of the variational convergence theory. 1. Introduction. Let H be a real Hilbert space and T be a maximal monotone operator on H. We consider the problem (P) “To find x ∈ H such that 0 ∈ Tx.” The practical importance of this problem is well known, thanks to its application