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arXiv · 2411.11628

Linear Convergence of the Proximal Gradient Method for Composite Optimization Under the Polyak-{\L}ojasiewicz Inequality and Its Variant

Qingyuan Kong·Rujun Jiang·Yihan He
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Abstract

We study the linear convergence rates of the proximal gradient method for composite functions satisfying two classes of Polyak-{\L}ojasiewicz (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.

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Qingyuan Kong, Rujun Jiang, Yihan He. 2024-11-18. Linear Convergence of the Proximal Gradient Method for Composite Optimization Under the Polyak-{\L}ojasiewicz Inequality and Its Variant. https://arxiv.org/abs/2411.11628

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