A proximal subgradient algorithm with extrapolation for structured nonconvex nonsmooth problems
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2022
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866929520943038464 |
|---|---|
| author | Pham, Tan Nhat Dao, Minh N. Shah, Rakibuzzaman Sultanova, Nargiz Li, Guoyin Islam, Syed |
| author_facet | Pham, Tan Nhat Dao, Minh N. Shah, Rakibuzzaman Sultanova, Nargiz Li, Guoyin Islam, Syed |
| contents | In this paper, we consider a class of structured nonconvex nonsmooth optimization problems, in which the objective function is formed by the sum of a possibly nonsmooth nonconvex function and a differentiable function whose gradient is Lipschitz continuous, subtracted by a weakly convex function. This type of structured problems has many practical applications in machine learning and statistics such as compressed sensing, signal recovery, sparse dictionary learning, clustering, matrix factorization, and others. We develop a flexible extrapolated proximal subgradient algorithm for solving these problems with guaranteed subsequential convergence to a stationary point. The global convergence of the whole sequence generated by our algorithm is also established under the Kurdyka-Lojasiewicz property. To illustrate the promising numerical performance of the proposed algorithm, we conduct numerical experiments on two important nonconvex models. This includes a least squares problem with a nonconvex regularization and an optimal power flow problem with distributed energy resources. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_12432 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A proximal subgradient algorithm with extrapolation for structured nonconvex nonsmooth problems Pham, Tan Nhat Dao, Minh N. Shah, Rakibuzzaman Sultanova, Nargiz Li, Guoyin Islam, Syed Optimization and Control 90C26, 49M27, 65K05 In this paper, we consider a class of structured nonconvex nonsmooth optimization problems, in which the objective function is formed by the sum of a possibly nonsmooth nonconvex function and a differentiable function whose gradient is Lipschitz continuous, subtracted by a weakly convex function. This type of structured problems has many practical applications in machine learning and statistics such as compressed sensing, signal recovery, sparse dictionary learning, clustering, matrix factorization, and others. We develop a flexible extrapolated proximal subgradient algorithm for solving these problems with guaranteed subsequential convergence to a stationary point. The global convergence of the whole sequence generated by our algorithm is also established under the Kurdyka-Lojasiewicz property. To illustrate the promising numerical performance of the proposed algorithm, we conduct numerical experiments on two important nonconvex models. This includes a least squares problem with a nonconvex regularization and an optimal power flow problem with distributed energy resources. |
| title | A proximal subgradient algorithm with extrapolation for structured nonconvex nonsmooth problems |
| topic | Optimization and Control 90C26, 49M27, 65K05 |
| url | https://arxiv.org/abs/2208.12432 |