On a fixed-point continuation method for a convex optimization problem
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arXiv
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| Format: | Preprint |
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2022
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| author | Fest, Jean-Baptiste Heikkilä, Tommi Loris, Ignace Martin, Ségolène Ratti, Luca Rebegoldi, Simone Sarnighausen, Gesa |
| author_facet | Fest, Jean-Baptiste Heikkilä, Tommi Loris, Ignace Martin, Ségolène Ratti, Luca Rebegoldi, Simone Sarnighausen, Gesa |
| contents | We consider a variation of the classical proximal-gradient algorithm for the iterative minimization of a cost function consisting of a sum of two terms, one smooth and the other prox-simple, and whose relative weight is determined by a penalty parameter. This so-called fixed-point continuation method allows one to approximate the problem's trade-off curve, i.e. to compute the minimizers of the cost function for a whole range of values of the penalty parameter at once. The algorithm is shown to converge, and a rate of convergence of the cost function is also derived. Furthermore, it is shown that this method is related to iterative algorithms constructed on the basis of the $ε$-subdifferential of the prox-simple term. Some numerical examples are provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_12256 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On a fixed-point continuation method for a convex optimization problem Fest, Jean-Baptiste Heikkilä, Tommi Loris, Ignace Martin, Ségolène Ratti, Luca Rebegoldi, Simone Sarnighausen, Gesa Optimization and Control Numerical Analysis We consider a variation of the classical proximal-gradient algorithm for the iterative minimization of a cost function consisting of a sum of two terms, one smooth and the other prox-simple, and whose relative weight is determined by a penalty parameter. This so-called fixed-point continuation method allows one to approximate the problem's trade-off curve, i.e. to compute the minimizers of the cost function for a whole range of values of the penalty parameter at once. The algorithm is shown to converge, and a rate of convergence of the cost function is also derived. Furthermore, it is shown that this method is related to iterative algorithms constructed on the basis of the $ε$-subdifferential of the prox-simple term. Some numerical examples are provided. |
| title | On a fixed-point continuation method for a convex optimization problem |
| topic | Optimization and Control Numerical Analysis |
| url | https://arxiv.org/abs/2212.12256 |