A feasible smoothing accelerated projected gradient method for nonsmooth convex optimization
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909589093482496 |
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| author | Nishioka, Akatsuki Kanno, Yoshihiro |
| author_facet | Nishioka, Akatsuki Kanno, Yoshihiro |
| contents | Smoothing accelerated gradient methods achieve faster convergence rates than that of the subgradient method for some nonsmooth convex optimization problems. However, Nesterov's extrapolation may require gradients at infeasible points, and thus they cannot be applied to some structural optimization problems. We introduce a variant of smoothing accelerated projected gradient methods where every variable is feasible. The $O(k^{-1}\log k)$ convergence rate is obtained using the Lyapunov function. We conduct a numerical experiment on the robust compliance optimization of a truss structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_07050 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A feasible smoothing accelerated projected gradient method for nonsmooth convex optimization Nishioka, Akatsuki Kanno, Yoshihiro Optimization and Control 90C25, 90C90 Smoothing accelerated gradient methods achieve faster convergence rates than that of the subgradient method for some nonsmooth convex optimization problems. However, Nesterov's extrapolation may require gradients at infeasible points, and thus they cannot be applied to some structural optimization problems. We introduce a variant of smoothing accelerated projected gradient methods where every variable is feasible. The $O(k^{-1}\log k)$ convergence rate is obtained using the Lyapunov function. We conduct a numerical experiment on the robust compliance optimization of a truss structure. |
| title | A feasible smoothing accelerated projected gradient method for nonsmooth convex optimization |
| topic | Optimization and Control 90C25, 90C90 |
| url | https://arxiv.org/abs/2312.07050 |