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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2004.00083 |
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| _version_ | 1866929314280243200 |
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| author | Themelis, Andreas Hermans, Ben Patrinos, Panagiotis |
| author_facet | Themelis, Andreas Hermans, Ben Patrinos, Panagiotis |
| contents | Difference-of-convex (DC) optimization problems are shown to be equivalent to the minimization of a Lipschitz-differentiable "envelope". A gradient method on this surrogate function yields a novel (sub)gradient-free proximal algorithm which is inherently parallelizable and can handle fully nonsmooth formulations. Newton-type methods such as L-BFGS are directly applicable with a classical linesearch. Our analysis reveals a deep kinship between the novel DC envelope and the forward-backward envelope, the former being a smooth and convexity-preserving nonlinear reparametrization of the latter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_00083 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A new envelope function for nonsmooth DC optimization Themelis, Andreas Hermans, Ben Patrinos, Panagiotis Optimization and Control 90C26, 90C53, 90C06 Difference-of-convex (DC) optimization problems are shown to be equivalent to the minimization of a Lipschitz-differentiable "envelope". A gradient method on this surrogate function yields a novel (sub)gradient-free proximal algorithm which is inherently parallelizable and can handle fully nonsmooth formulations. Newton-type methods such as L-BFGS are directly applicable with a classical linesearch. Our analysis reveals a deep kinship between the novel DC envelope and the forward-backward envelope, the former being a smooth and convexity-preserving nonlinear reparametrization of the latter. |
| title | A new envelope function for nonsmooth DC optimization |
| topic | Optimization and Control 90C26, 90C53, 90C06 |
| url | https://arxiv.org/abs/2004.00083 |