Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.03506 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908351906971648 |
|---|---|
| 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 |