Approximate Bregman Proximal Gradient Algorithm for Relatively Smooth Nonconvex Optimization
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913582945402880 |
|---|---|
| author | Takahashi, Shota Takeda, Akiko |
| author_facet | Takahashi, Shota Takeda, Akiko |
| contents | In this paper, we propose the approximate Bregman proximal gradient algorithm (ABPG) for solving composite nonconvex optimization problems. ABPG employs a new distance that approximates the Bregman distance, making the subproblem of ABPG simpler to solve compared to existing Bregman-type algorithms. The subproblem of ABPG is often expressed in a closed form. Similarly to existing Bregman-type algorithms, ABPG does not require the global Lipschitz continuity for the gradient of the smooth part. Instead, assuming the smooth adaptable property, we establish the global subsequential convergence under standard assumptions. Additionally, assuming that the Kurdyka--Łojasiewicz property holds, we prove the global convergence for a special case. Our numerical experiments on the $\ell_p$ regularized least squares problem, the $\ell_p$ loss problem, and the nonnegative linear system show that ABPG outperforms existing algorithms especially when the gradient of the smooth part is not globally Lipschitz or even local Lipschitz continuous. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_07847 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Approximate Bregman Proximal Gradient Algorithm for Relatively Smooth Nonconvex Optimization Takahashi, Shota Takeda, Akiko Optimization and Control 90C26, 49M37, 65K05 In this paper, we propose the approximate Bregman proximal gradient algorithm (ABPG) for solving composite nonconvex optimization problems. ABPG employs a new distance that approximates the Bregman distance, making the subproblem of ABPG simpler to solve compared to existing Bregman-type algorithms. The subproblem of ABPG is often expressed in a closed form. Similarly to existing Bregman-type algorithms, ABPG does not require the global Lipschitz continuity for the gradient of the smooth part. Instead, assuming the smooth adaptable property, we establish the global subsequential convergence under standard assumptions. Additionally, assuming that the Kurdyka--Łojasiewicz property holds, we prove the global convergence for a special case. Our numerical experiments on the $\ell_p$ regularized least squares problem, the $\ell_p$ loss problem, and the nonnegative linear system show that ABPG outperforms existing algorithms especially when the gradient of the smooth part is not globally Lipschitz or even local Lipschitz continuous. |
| title | Approximate Bregman Proximal Gradient Algorithm for Relatively Smooth Nonconvex Optimization |
| topic | Optimization and Control 90C26, 49M37, 65K05 |
| url | https://arxiv.org/abs/2311.07847 |