# Perturbed Proximal Point Algorithm with Nonquadratic Kernel

Serdica Mathematical Journal (2000)

- Volume: 26, Issue: 3, page 177-206
- ISSN: 1310-6600

## Access Full Article

top## Abstract

top## How to cite

topBrohe, M., and Tossings, P.. "Perturbed Proximal Point Algorithm with Nonquadratic Kernel." Serdica Mathematical Journal 26.3 (2000): 177-206. <http://eudml.org/doc/11488>.

@article{Brohe2000,

abstract = {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.},

author = {Brohe, M., Tossings, P.},

journal = {Serdica Mathematical Journal},

keywords = {Proximal Point Algorithm; Bregman Functions; Generalized Resolvent Operator; Variational Convergence; proximal point algorithm; Bregman functions; generalized resolvent operator; variational convergence},

language = {eng},

number = {3},

pages = {177-206},

publisher = {Institute of Mathematics and Informatics},

title = {Perturbed Proximal Point Algorithm with Nonquadratic Kernel},

url = {http://eudml.org/doc/11488},

volume = {26},

year = {2000},

}

TY - JOUR

AU - Brohe, M.

AU - Tossings, P.

TI - Perturbed Proximal Point Algorithm with Nonquadratic Kernel

JO - Serdica Mathematical Journal

PY - 2000

PB - Institute of Mathematics and Informatics

VL - 26

IS - 3

SP - 177

EP - 206

AB - 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.

LA - eng

KW - Proximal Point Algorithm; Bregman Functions; Generalized Resolvent Operator; Variational Convergence; proximal point algorithm; Bregman functions; generalized resolvent operator; variational convergence

UR - http://eudml.org/doc/11488

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.