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Main Authors: Chen, Xiaojun, Kelley, C. T., Wang, Lei
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2505.03506
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author Chen, Xiaojun
Kelley, C. T.
Wang, Lei
author_facet Chen, Xiaojun
Kelley, C. T.
Wang, Lei
contents In this paper, we present a new complexity result for the gradient descent method with an appropriately fixed stepsize for minimizing a strongly convex function with locally $α$-H{ö}lder continuous gradients ($0 < α\leq 1$). The complexity bound for finding an approximate minimizer with a distance to the true minimizer less than $\varepsilon$ is $O(\log (\varepsilon^{-1}) \varepsilon^{2 α- 2})$, which extends the well-known complexity result for $α= 1$.
format Preprint
id arxiv_https___arxiv_org_abs_2505_03506
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A New Complexity Result for Strongly Convex Optimization with Locally $α$-H{ö}lder Continuous Gradients
Chen, Xiaojun
Kelley, C. T.
Wang, Lei
Optimization and Control
In this paper, we present a new complexity result for the gradient descent method with an appropriately fixed stepsize for minimizing a strongly convex function with locally $α$-H{ö}lder continuous gradients ($0 < α\leq 1$). The complexity bound for finding an approximate minimizer with a distance to the true minimizer less than $\varepsilon$ is $O(\log (\varepsilon^{-1}) \varepsilon^{2 α- 2})$, which extends the well-known complexity result for $α= 1$.
title A New Complexity Result for Strongly Convex Optimization with Locally $α$-H{ö}lder Continuous Gradients
topic Optimization and Control
url https://arxiv.org/abs/2505.03506