A PVT-Type Algorithm for Minimizing a Nonsmooth Convex Function

Pang, Li-Ping, and Xia, Zun-Quan. "A PVT-Type Algorithm for Minimizing a Nonsmooth Convex Function." Serdica Mathematical Journal 29.1 (2003): 11-32. <http://eudml.org/doc/219657>.

@article{Pang2003,
abstract = {2000 Mathematics Subject Classification: 90C25, 68W10, 49M37.A general framework of the (parallel variable transformation) PVT-type algorithm, called the PVT-MYR algorithm, for minimizing a non-smooth convex function is proposed, via the Moreau-Yosida regularization. As a particular scheme of this framework an ε-scheme is also presented. The global convergence of this algorithm is given under the assumptions of strong convexity of the objective function and an ε-descent condition determined by an ε-forced function. An appendix stating the proximal point algorithm is recalled in the last section.},
author = {Pang, Li-Ping, Xia, Zun-Quan},
journal = {Serdica Mathematical Journal},
keywords = {Parallel Algorithm; Synchronous Parallel; Convex Minimization; Moreau-Yosida Regularization; Strong Convexity; Descent Condition; Forced Function; algorithms; Moreau-Yosida regularization; nonsmooth convex function; parallel variable transformation; global convergence},
language = {eng},
number = {1},
pages = {11-32},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {A PVT-Type Algorithm for Minimizing a Nonsmooth Convex Function},
url = {http://eudml.org/doc/219657},
volume = {29},
year = {2003},
}

TY - JOUR
AU - Pang, Li-Ping
AU - Xia, Zun-Quan
TI - A PVT-Type Algorithm for Minimizing a Nonsmooth Convex Function
JO - Serdica Mathematical Journal
PY - 2003
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 29
IS - 1
SP - 11
EP - 32
AB - 2000 Mathematics Subject Classification: 90C25, 68W10, 49M37.A general framework of the (parallel variable transformation) PVT-type algorithm, called the PVT-MYR algorithm, for minimizing a non-smooth convex function is proposed, via the Moreau-Yosida regularization. As a particular scheme of this framework an ε-scheme is also presented. The global convergence of this algorithm is given under the assumptions of strong convexity of the objective function and an ε-descent condition determined by an ε-forced function. An appendix stating the proximal point algorithm is recalled in the last section.
LA - eng
KW - Parallel Algorithm; Synchronous Parallel; Convex Minimization; Moreau-Yosida Regularization; Strong Convexity; Descent Condition; Forced Function; algorithms; Moreau-Yosida regularization; nonsmooth convex function; parallel variable transformation; global convergence
UR - http://eudml.org/doc/219657
ER -