Hybrid extragradient proximal algorithm coupled with parametric approximation and penalty/barrier methods.

Miguel Carrasco

doi:10.1080/02331934.2011.592528

Hybrid extragradient proximal algorithm coupled with parametric approximation and penalty/barrier methods.

Miguel Carrasco^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

In this article we study the hybrid extragradient method coupled with approximation and penalty schemes for convex minimization problems. Under certain hypotheses, which include, for example, the case of Tikhonov regularization, we prove asymptotic convergence of the method to the solution set of our minimization problem. When we use schemes of penalization or barrier, we can show asymptotic convergence using the well-known fast/slow parameterization techniques and exploiting the existence and finite length of an optimal path.

Original language	English
Pages (from-to)	397-414
Number of pages	18
Journal	Optimization
Volume	62
Issue number	3
DOIs	https://doi.org/10.1080/02331934.2011.592528
State	Published - Mar 2013

Bibliographical note

Funding Information:
The author thanks Felipe Alvarez from Universidad de Chile and Lionel Thibault from Université de Montpellier 2, France, for useful discussions on this subjects. The author was partially supported by FONDECYT grant no. 11090328.

Keywords

convex optimization
global convergence
hybrid method
parametric approximation
proximal point

Access to Document

10.1080/02331934.2011.592528

Cite this

@article{9295acc5d6a44938bd731333f0b41b72,

title = "Hybrid extragradient proximal algorithm coupled with parametric approximation and penalty/barrier methods.",

abstract = "In this article we study the hybrid extragradient method coupled with approximation and penalty schemes for convex minimization problems. Under certain hypotheses, which include, for example, the case of Tikhonov regularization, we prove asymptotic convergence of the method to the solution set of our minimization problem. When we use schemes of penalization or barrier, we can show asymptotic convergence using the well-known fast/slow parameterization techniques and exploiting the existence and finite length of an optimal path.",

keywords = "convex optimization, global convergence, hybrid method, parametric approximation, proximal point, global convergence, parametric approximation, hybrid method, convex optimization",

author = "Miguel Carrasco",

note = "Funding Information: The author thanks Felipe Alvarez from Universidad de Chile and Lionel Thibault from Universit{\'e} de Montpellier 2, France, for useful discussions on this subjects. The author was partially supported by FONDECYT grant no. 11090328.",

year = "2013",

month = mar,

doi = "10.1080/02331934.2011.592528",

language = "English",

volume = "62",

pages = "397--414",

journal = "Optimization",

issn = "0233-1934",

publisher = "Taylor and Francis Ltd.",

number = "3",

}

TY - JOUR

T1 - Hybrid extragradient proximal algorithm coupled with parametric approximation and penalty/barrier methods.

AU - Carrasco, Miguel

N1 - Funding Information: The author thanks Felipe Alvarez from Universidad de Chile and Lionel Thibault from Université de Montpellier 2, France, for useful discussions on this subjects. The author was partially supported by FONDECYT grant no. 11090328.

PY - 2013/3

Y1 - 2013/3

N2 - In this article we study the hybrid extragradient method coupled with approximation and penalty schemes for convex minimization problems. Under certain hypotheses, which include, for example, the case of Tikhonov regularization, we prove asymptotic convergence of the method to the solution set of our minimization problem. When we use schemes of penalization or barrier, we can show asymptotic convergence using the well-known fast/slow parameterization techniques and exploiting the existence and finite length of an optimal path.

AB - In this article we study the hybrid extragradient method coupled with approximation and penalty schemes for convex minimization problems. Under certain hypotheses, which include, for example, the case of Tikhonov regularization, we prove asymptotic convergence of the method to the solution set of our minimization problem. When we use schemes of penalization or barrier, we can show asymptotic convergence using the well-known fast/slow parameterization techniques and exploiting the existence and finite length of an optimal path.

KW - convex optimization

KW - global convergence

KW - hybrid method

KW - parametric approximation

KW - proximal point

KW - global convergence

KW - parametric approximation

KW - hybrid method

KW - convex optimization

UR - http://www.scopus.com/inward/record.url?scp=84874501986&partnerID=8YFLogxK

U2 - 10.1080/02331934.2011.592528

DO - 10.1080/02331934.2011.592528

M3 - Article

AN - SCOPUS:84874501986

SN - 0233-1934

VL - 62

SP - 397

EP - 414

JO - Optimization

JF - Optimization

IS - 3

ER -

Hybrid extragradient proximal algorithm coupled with parametric approximation and penalty/barrier methods.

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this