The CoMirror algorithm for solving nonsmooth constrained convex problems

Amir Beck; Aharon Ben-Tal; Nili Guttmann-Beck; Luba Tetruashvili

doi:10.1016/j.orl.2010.08.005

The CoMirror algorithm for solving nonsmooth constrained convex problems

Amir Beck^*, Aharon Ben-Tal, Nili Guttmann-Beck, Luba Tetruashvili

^*Corresponding author for this work

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

27 Scopus citations

Abstract

We introduce a first-order Mirror-Descent (MD) type algorithm for solving nondifferentiable convex problems having a combination of simple constraint set X (ball, simplex, etc.) and an additional functional constraint. The method is tuned to exploit the structure of X by employing an appropriate non-Euclidean distance-like function. Convergence results and efficiency estimates are derived. The performance of the algorithm is demonstrated by solving certain image deblurring problems.

Original language	English
Pages (from-to)	493-498
Number of pages	6
Journal	Operations Research Letters
Volume	38
Issue number	6
DOIs	https://doi.org/10.1016/j.orl.2010.08.005
State	Published - Nov 2010
Externally published	Yes

Keywords

Convex optimization
Gradient-based methods
Mirror Descent
Non-Euclidean projection

Access to Document

10.1016/j.orl.2010.08.005

Cite this

@article{7f3e311beaac40b49c80c2eb1a81abfa,

title = "The CoMirror algorithm for solving nonsmooth constrained convex problems",

abstract = "We introduce a first-order Mirror-Descent (MD) type algorithm for solving nondifferentiable convex problems having a combination of simple constraint set X (ball, simplex, etc.) and an additional functional constraint. The method is tuned to exploit the structure of X by employing an appropriate non-Euclidean distance-like function. Convergence results and efficiency estimates are derived. The performance of the algorithm is demonstrated by solving certain image deblurring problems.",

keywords = "Convex optimization, Gradient-based methods, Mirror Descent, Non-Euclidean projection",

author = "Amir Beck and Aharon Ben-Tal and Nili Guttmann-Beck and Luba Tetruashvili",

year = "2010",

month = nov,

doi = "10.1016/j.orl.2010.08.005",

language = "אנגלית",

volume = "38",

pages = "493--498",

journal = "Operations Research Letters",

issn = "0167-6377",

publisher = "Elsevier B.V.",

number = "6",

}

TY - JOUR

T1 - The CoMirror algorithm for solving nonsmooth constrained convex problems

AU - Beck, Amir

AU - Ben-Tal, Aharon

AU - Guttmann-Beck, Nili

AU - Tetruashvili, Luba

PY - 2010/11

Y1 - 2010/11

N2 - We introduce a first-order Mirror-Descent (MD) type algorithm for solving nondifferentiable convex problems having a combination of simple constraint set X (ball, simplex, etc.) and an additional functional constraint. The method is tuned to exploit the structure of X by employing an appropriate non-Euclidean distance-like function. Convergence results and efficiency estimates are derived. The performance of the algorithm is demonstrated by solving certain image deblurring problems.

AB - We introduce a first-order Mirror-Descent (MD) type algorithm for solving nondifferentiable convex problems having a combination of simple constraint set X (ball, simplex, etc.) and an additional functional constraint. The method is tuned to exploit the structure of X by employing an appropriate non-Euclidean distance-like function. Convergence results and efficiency estimates are derived. The performance of the algorithm is demonstrated by solving certain image deblurring problems.

KW - Convex optimization

KW - Gradient-based methods

KW - Mirror Descent

KW - Non-Euclidean projection

UR - http://www.scopus.com/inward/record.url?scp=77958104027&partnerID=8YFLogxK

U2 - 10.1016/j.orl.2010.08.005

DO - 10.1016/j.orl.2010.08.005

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:77958104027

SN - 0167-6377

VL - 38

SP - 493

EP - 498

JO - Operations Research Letters

JF - Operations Research Letters

IS - 6

ER -

The CoMirror algorithm for solving nonsmooth constrained convex problems

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this