# A PVT-Type Algorithm for Minimizing a Nonsmooth Convex Function

Serdica Mathematical Journal (2003)

- Volume: 29, Issue: 1, page 11-32
- ISSN: 1310-6600

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topPang, 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 -

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