Barrier Algorithms for Constrained Non-Convex Optimization
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913334395142144 |
|---|---|
| author | Dvurechensky, Pavel Staudigl, Mathias |
| author_facet | Dvurechensky, Pavel Staudigl, Mathias |
| contents | In this paper we theoretically show that interior-point methods based on self-concordant barriers possess favorable global complexity beyond their standard application area of convex optimization. To do that we propose first- and second-order methods for non-convex optimization problems with general convex set constraints and linear constraints. Our methods attain a suitably defined class of approximate first- or second-order KKT points with the worst-case iteration complexity similar to unconstrained problems, namely $O(\varepsilon^{-2})$ (first-order) and $O(\varepsilon^{-3/2})$ (second-order), respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18724 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Barrier Algorithms for Constrained Non-Convex Optimization Dvurechensky, Pavel Staudigl, Mathias Optimization and Control 90C26, 90C30, 90C60, 68Q25 G.1.6 In this paper we theoretically show that interior-point methods based on self-concordant barriers possess favorable global complexity beyond their standard application area of convex optimization. To do that we propose first- and second-order methods for non-convex optimization problems with general convex set constraints and linear constraints. Our methods attain a suitably defined class of approximate first- or second-order KKT points with the worst-case iteration complexity similar to unconstrained problems, namely $O(\varepsilon^{-2})$ (first-order) and $O(\varepsilon^{-3/2})$ (second-order), respectively. |
| title | Barrier Algorithms for Constrained Non-Convex Optimization |
| topic | Optimization and Control 90C26, 90C30, 90C60, 68Q25 G.1.6 |
| url | https://arxiv.org/abs/2404.18724 |