Linear Convergence of the Proximal Gradient Method for Composite Optimization Under the Polyak-Łojasiewicz Inequality and Its Variant

Fuente: arXiv
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Main Authors: Kong, Qingyuan, Jiang, Rujun, He, Yihan
Format: Preprint
Published: 2024
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author Kong, Qingyuan
Jiang, Rujun
He, Yihan
author_facet Kong, Qingyuan
Jiang, Rujun
He, Yihan
contents We study the linear convergence rates of the proximal gradient method for composite functions satisfying two classes of Polyak-Łojasiewicz (PL) inequality: the PL inequality, the variant of PL inequality defined by the proximal map-based residual. Using the performance estimation problem, we either provide new explicit linear convergence rates or improve existing complexity bounds for minimizing composite functions under the two classes of PL inequality. Finally, we illustrate numerically the effects of our theoretical results.
format Preprint
id arxiv_https___arxiv_org_abs_2411_11628
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Linear Convergence of the Proximal Gradient Method for Composite Optimization Under the Polyak-Łojasiewicz Inequality and Its Variant
Kong, Qingyuan
Jiang, Rujun
He, Yihan
Optimization and Control
We study the linear convergence rates of the proximal gradient method for composite functions satisfying two classes of Polyak-Łojasiewicz (PL) inequality: the PL inequality, the variant of PL inequality defined by the proximal map-based residual. Using the performance estimation problem, we either provide new explicit linear convergence rates or improve existing complexity bounds for minimizing composite functions under the two classes of PL inequality. Finally, we illustrate numerically the effects of our theoretical results.
title Linear Convergence of the Proximal Gradient Method for Composite Optimization Under the Polyak-Łojasiewicz Inequality and Its Variant
topic Optimization and Control
url https://arxiv.org/abs/2411.11628