Perturbed Proximal Point Algorithm with Nonquadratic Kernel
Serdica Mathematical Journal, Tome 26 (2000) no. 3, pp. 177-206
Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library
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 [16], for solving
the problem
(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.
Keywords:
Proximal Point Algorithm, Bregman Functions, Generalized Resolvent Operator, Variational Convergence
@article{SMJ2_2000_26_3_a0,
author = {Brohe, M. and Tossings, P.},
title = {Perturbed {Proximal} {Point} {Algorithm} with {Nonquadratic} {Kernel}},
journal = {Serdica Mathematical Journal},
pages = {177--206},
publisher = {mathdoc},
volume = {26},
number = {3},
year = {2000},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SMJ2_2000_26_3_a0/}
}
Brohe, M.; Tossings, P. Perturbed Proximal Point Algorithm with Nonquadratic Kernel. Serdica Mathematical Journal, Tome 26 (2000) no. 3, pp. 177-206. http://geodesic.mathdoc.fr/item/SMJ2_2000_26_3_a0/