Accelerated primal dual fixed point algorithm
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908624382590976 |
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| author | Zhu, Ya-Nan |
| author_facet | Zhu, Ya-Nan |
| contents | This work proposes an Accelerated Primal-Dual Fixed-Point (APDFP) method that employs Nesterov type acceleration to solve composite problems of the form min f(x) + g(Bx), where g is nonsmooth and B is a linear operator. The APDFP features fully decoupled iterations and can be regarded as a generalization of Nesterov's accelerated gradient in the setting where B can be a non-identity matrix. Theoretically, we improve the convergence rate of the partial primal-dual gap with respect to the Lipschitz constant of the gradient of f from O(1/k) to O(1/k^2). Numerical experiments on graph-guided logistic regression and CT image reconstruction are conducted to validate the correctness and demonstrate the efficiency of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_00385 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Accelerated primal dual fixed point algorithm Zhu, Ya-Nan Optimization and Control 90C25, 49M29, 65K05, 65Y20, 68U10 This work proposes an Accelerated Primal-Dual Fixed-Point (APDFP) method that employs Nesterov type acceleration to solve composite problems of the form min f(x) + g(Bx), where g is nonsmooth and B is a linear operator. The APDFP features fully decoupled iterations and can be regarded as a generalization of Nesterov's accelerated gradient in the setting where B can be a non-identity matrix. Theoretically, we improve the convergence rate of the partial primal-dual gap with respect to the Lipschitz constant of the gradient of f from O(1/k) to O(1/k^2). Numerical experiments on graph-guided logistic regression and CT image reconstruction are conducted to validate the correctness and demonstrate the efficiency of the proposed method. |
| title | Accelerated primal dual fixed point algorithm |
| topic | Optimization and Control 90C25, 49M29, 65K05, 65Y20, 68U10 |
| url | https://arxiv.org/abs/2511.00385 |