arXiv Open Access 2024

A Proof of Exact Convergence Rate of Gradient Descent. Part I. Performance Criterion $\Vert \nabla f(x_N)\Vert^2/(f(x_0)-f_*)$

Jungbin Kim

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Abstrak

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].

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math.OC

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Jungbin Kim

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Kim, J. (2024). A Proof of Exact Convergence Rate of Gradient Descent. Part I. Performance Criterion $\Vert \nabla f(x_N)\Vert^2/(f(x_0)-f_*)$. https://arxiv.org/abs/2412.04435

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Tahun Terbit: 2024
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓