Convergence analysis of a primal-dual optimization-by-continuation algorithm
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866929525111128064 |
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| author | Loris, Ignace Rebegoldi, Simone |
| author_facet | Loris, Ignace Rebegoldi, Simone |
| contents | We present a numerical iterative optimization algorithm for the minimization of a cost function consisting of a linear combination of three convex terms, one of which is differentiable, a second one is prox-simple and the third one is the composition of a linear map and a prox-simple function. The algorithm's special feature lies in its ability to approximate, in a single iteration run, the minimizers of the cost function for many different values of the parameters determining the relative weight of the three terms in the cost function. A proof of convergence of the algorithm, based on an inexact variable metric approach, is also provided. As a special case, one recovers a generalization of the primal-dual algorithm of Chambolle and Pock, and also of the proximal-gradient algorithm. Finally, we show how it is related to a primal-dual iterative algorithm based on inexact proximal evaluations of the non-smooth terms of the cost function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_09123 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Convergence analysis of a primal-dual optimization-by-continuation algorithm Loris, Ignace Rebegoldi, Simone Optimization and Control Numerical Analysis 90C06, 90C25, 90C59, 90C90, 49M29, 65K10 We present a numerical iterative optimization algorithm for the minimization of a cost function consisting of a linear combination of three convex terms, one of which is differentiable, a second one is prox-simple and the third one is the composition of a linear map and a prox-simple function. The algorithm's special feature lies in its ability to approximate, in a single iteration run, the minimizers of the cost function for many different values of the parameters determining the relative weight of the three terms in the cost function. A proof of convergence of the algorithm, based on an inexact variable metric approach, is also provided. As a special case, one recovers a generalization of the primal-dual algorithm of Chambolle and Pock, and also of the proximal-gradient algorithm. Finally, we show how it is related to a primal-dual iterative algorithm based on inexact proximal evaluations of the non-smooth terms of the cost function. |
| title | Convergence analysis of a primal-dual optimization-by-continuation algorithm |
| topic | Optimization and Control Numerical Analysis 90C06, 90C25, 90C59, 90C90, 49M29, 65K10 |
| url | https://arxiv.org/abs/2311.09123 |