Local properties and augmented Lagrangians in fully nonconvex composite optimization
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914901698543616 |
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| author | De Marchi, Alberto Mehlitz, Patrick |
| author_facet | De Marchi, Alberto Mehlitz, Patrick |
| contents | A broad class of optimization problems can be cast in composite form, that is, considering the minimization of the composition of a lower semicontinuous function with a differentiable mapping. This paper investigates the versatile template of composite optimization without any convexity assumptions. First- and second-order optimality conditions are discussed. We highlight the difficulties that stem from the lack of convexity when dealing with necessary conditions in a Lagrangian framework and when considering error bounds. Building upon these characterizations, a local convergence analysis is delineated for a recently developed augmented Lagrangian method, deriving rates of convergence in the fully nonconvex setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_01980 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Local properties and augmented Lagrangians in fully nonconvex composite optimization De Marchi, Alberto Mehlitz, Patrick Optimization and Control 49J52, 49J53, 65K10, 90C30, 90C33 A broad class of optimization problems can be cast in composite form, that is, considering the minimization of the composition of a lower semicontinuous function with a differentiable mapping. This paper investigates the versatile template of composite optimization without any convexity assumptions. First- and second-order optimality conditions are discussed. We highlight the difficulties that stem from the lack of convexity when dealing with necessary conditions in a Lagrangian framework and when considering error bounds. Building upon these characterizations, a local convergence analysis is delineated for a recently developed augmented Lagrangian method, deriving rates of convergence in the fully nonconvex setting. |
| title | Local properties and augmented Lagrangians in fully nonconvex composite optimization |
| topic | Optimization and Control 49J52, 49J53, 65K10, 90C30, 90C33 |
| url | https://arxiv.org/abs/2309.01980 |