The Perturbed Generalized Proximal Point Algorithm

During the last years, different modifications were introduced in the proximal point algorithm developed by R.T. Rockafellar for searching a zero of a maximal monotone operator on a real Hilbert space. We combine these modifications to get a new version of this algorithm. We take simultaneously into account a variable metric, a perturbation and a kind of relaxation. Our work takes place in the context of the variational convergence theory.