A search-free $O(1/k^{3/2})$ homotopy inexact proximal-Newton extragradient algorithm for monotone variational inequalities
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913312700104704 |
|---|---|
| author | Alves, M. Marques Pereira, João M. Svaiter, Benar F. |
| author_facet | Alves, M. Marques Pereira, João M. Svaiter, Benar F. |
| contents | We present and study the iteration-complexity of a relative-error inexact proximal-Newton extragradient algorithm for solving smooth monotone variational inequality problems in real Hilbert spaces. We removed a search procedure from Monteiro and Svaiter (2012) by introducing a novel approach based on homotopy, which requires the resolution (at each iteration) of a single strongly monotone linear variational inequality. For a given tolerance $ρ>0$, our main algorithm exhibits pointwise $O\left(\frac{1}ρ\right)$ and ergodic $O\left(\frac{1}{ρ^{2/3}}\right)$ iteration-complexities. From a practical perspective, preliminary numerical experiments indicate that our main algorithm outperforms some previous proximal-Newton schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_05887 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A search-free $O(1/k^{3/2})$ homotopy inexact proximal-Newton extragradient algorithm for monotone variational inequalities Alves, M. Marques Pereira, João M. Svaiter, Benar F. Optimization and Control 49M15, 90C06, 68Q25, 47N10 We present and study the iteration-complexity of a relative-error inexact proximal-Newton extragradient algorithm for solving smooth monotone variational inequality problems in real Hilbert spaces. We removed a search procedure from Monteiro and Svaiter (2012) by introducing a novel approach based on homotopy, which requires the resolution (at each iteration) of a single strongly monotone linear variational inequality. For a given tolerance $ρ>0$, our main algorithm exhibits pointwise $O\left(\frac{1}ρ\right)$ and ergodic $O\left(\frac{1}{ρ^{2/3}}\right)$ iteration-complexities. From a practical perspective, preliminary numerical experiments indicate that our main algorithm outperforms some previous proximal-Newton schemes. |
| title | A search-free $O(1/k^{3/2})$ homotopy inexact proximal-Newton extragradient algorithm for monotone variational inequalities |
| topic | Optimization and Control 49M15, 90C06, 68Q25, 47N10 |
| url | https://arxiv.org/abs/2308.05887 |