Perturbed Proximal Point Algorithm with Nonquadratic Kernel

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

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Abstract

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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.

How to cite

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Brohe, 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 -

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