Convergence rates of proximal gradient methods via the convex conjugate

David H. Gutman; Javier F. Pena

doi:10.1137/18M1164329

Convergence rates of proximal gradient methods via the convex conjugate

David H. Gutman, Javier F. Pena

Industrial Engineering

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

1 Scopus citations

Abstract

We give a novel proof of the O(1/k) and O(1/k ² ) convergence rates of the proximal gradient and accelerated proximal gradient methods for composite convex minimization. The crux of the new proof is an upper bound constructed via the convex conjugate of the objective function.

Original language	English
Pages (from-to)	162-174
Number of pages	13
Journal	SIAM Journal on Optimization
Volume	29
Issue number	1
DOIs	https://doi.org/10.1137/18M1164329
State	Published - 2019

Keywords

Acceleration
Convex conjugate
Proximal gradient

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title = "Convergence rates of proximal gradient methods via the convex conjugate",

abstract = " We give a novel proof of the O(1/k) and O(1/k 2 ) convergence rates of the proximal gradient and accelerated proximal gradient methods for composite convex minimization. The crux of the new proof is an upper bound constructed via the convex conjugate of the objective function. ",

keywords = "Acceleration, Convex conjugate, Proximal gradient",

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note = "Funding Information: This research was funded by NSF grant CMMI-1534850. Publisher Copyright: {\textcopyright} 2019 Society for Industrial and Applied Mathematics.",

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Convergence rates of proximal gradient methods via the convex conjugate

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Keywords

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