Perturbed Proximal Point Algorithm with Nonquadratic Kernel

Let H be a real Hilbert space and T be a maximal monotone operator on H. A well-known algorithm, developed by R.T. Rockafellar, for solving the problem "To find x in H such that 0 in Tx" is the proximal point algorithm. Several generalizations have been considered by several authors: introduction of a perturbation, introduction of a variable metric in the perturbed algorithm, introduction of a pseudo-metric in place of the classical regularization, ... We summarize several of these extensions by taking into account a pseudo-metric as regularization and a perturbation in an inexact version of the algorithm.