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17 February 2025

» arxiv » 2301.01530

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Nonlinear conjugate gradient methods: worst-case convergence rates via computer-assisted analyses
Shuvomoy Das Gupta ; Robert M. Freund ; Xu Andy Sun ; Adrien Taylor ;
Date:	4 Jan 2023
Abstract:	In this paper, we propose a computer-assisted approach to the analysis of the worst-case convergence of nonlinear conjugate gradient methods (NCGMs). Those methods are known for their generally good empirical performances for large-scale optimization, while having relatively incomplete analyses. Using this approach, we establish novel complexity bounds for the Polak-Ribi’ere-Polyak (PRP) and the Fletcher-Reeves (FR) NCGMs for smooth strongly convex minimization. Conversely, we provide examples showing that those methods might behave worse than the regular steepest descent on the same class of problems.
Source:	arXiv, 2301.01530
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