Variable smoothing algorithm for inner-loop-free DC composite optimizations
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915467163074560 |
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| author | Yazawa, Kumataro Kume, Keita Yamada, Isao |
| author_facet | Yazawa, Kumataro Kume, Keita Yamada, Isao |
| contents | We propose a variable smoothing algorithm for minimizing a nonsmooth and nonconvex cost function. The cost function is the sum of a smooth function and a composition of a difference-of-convex (DC) function with a smooth mapping. At each step of our algorithm, we generate a smooth surrogate function by using the Moreau envelope of each weakly convex function in the DC function, and then perform the gradient descent update of the surrogate function. The proposed algorithm does not require any inner loop unlike many existing algorithms for DC problem. We also present a convergence analysis in terms of a DC critical point for the proposed algorithm as well as its application to robust phase retrieval. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_13990 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Variable smoothing algorithm for inner-loop-free DC composite optimizations Yazawa, Kumataro Kume, Keita Yamada, Isao Optimization and Control We propose a variable smoothing algorithm for minimizing a nonsmooth and nonconvex cost function. The cost function is the sum of a smooth function and a composition of a difference-of-convex (DC) function with a smooth mapping. At each step of our algorithm, we generate a smooth surrogate function by using the Moreau envelope of each weakly convex function in the DC function, and then perform the gradient descent update of the surrogate function. The proposed algorithm does not require any inner loop unlike many existing algorithms for DC problem. We also present a convergence analysis in terms of a DC critical point for the proposed algorithm as well as its application to robust phase retrieval. |
| title | Variable smoothing algorithm for inner-loop-free DC composite optimizations |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2503.13990 |