Proximal Point Algorithm Bregman Functions Generalized Resolvent Operator Variational Convergence
Institute of Mathematics and Informatics
Serdica Mathematical Journal, Vol. 26, No 3, (2000), 177p-206p
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
(P) ”To find x ∈ H such that 0 ∈ T x”
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 some of these extensions by taking simultaneously into
account a pseudo-metric as regularization and a perturbation in an inexact
version of the algorithm.