A Proof of Exact Convergence Rate of Gradient Descent. Part I. Performance Criterion $\Vert \nabla f(x_N)\Vert^2/(f(x_0)-f_*)$
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912296087846912 |
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| author | Kim, Jungbin |
| author_facet | Kim, Jungbin |
| contents | We prove the exact worst-case convergence rate of gradient descent for smooth strongly convex optimization, with respect to the performance criterion $\Vert \nabla f(x_N)\Vert^2/(f(x_0)-f_*)$. The proof differs from the previous one by Rotaru \emph{et al.} [RGP24], and is based on the performance estimation methodology [DT14]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_04435 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Proof of Exact Convergence Rate of Gradient Descent. Part I. Performance Criterion $\Vert \nabla f(x_N)\Vert^2/(f(x_0)-f_*)$ Kim, Jungbin Optimization and Control We prove the exact worst-case convergence rate of gradient descent for smooth strongly convex optimization, with respect to the performance criterion $\Vert \nabla f(x_N)\Vert^2/(f(x_0)-f_*)$. The proof differs from the previous one by Rotaru \emph{et al.} [RGP24], and is based on the performance estimation methodology [DT14]. |
| title | A Proof of Exact Convergence Rate of Gradient Descent. Part I. Performance Criterion $\Vert \nabla f(x_N)\Vert^2/(f(x_0)-f_*)$ |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2412.04435 |