On the Moreau envelope properties of weakly convex functions
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917077509472256 |
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| author | Renaud, Marien Leclaire, Arthur Papadakis, Nicolas |
| author_facet | Renaud, Marien Leclaire, Arthur Papadakis, Nicolas |
| contents | In this document, we present the main properties satisfied by the Moreau envelope of weakly convex functions. The Moreau envelope has been introduced in convex optimization to regularize convex functionals while preserving their global minimizers. However, the Moreau envelope is also defined for the more general class of weakly convex function and can be a useful tool for optimization in this context. The main properties of the Moreau envelope have been demonstrated for convex functions and are generalized to weakly convex function in various works. This document summarizes the vast literature on the properties of the Moreau envelope and provides the associated proofs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13960 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Moreau envelope properties of weakly convex functions Renaud, Marien Leclaire, Arthur Papadakis, Nicolas Optimization and Control In this document, we present the main properties satisfied by the Moreau envelope of weakly convex functions. The Moreau envelope has been introduced in convex optimization to regularize convex functionals while preserving their global minimizers. However, the Moreau envelope is also defined for the more general class of weakly convex function and can be a useful tool for optimization in this context. The main properties of the Moreau envelope have been demonstrated for convex functions and are generalized to weakly convex function in various works. This document summarizes the vast literature on the properties of the Moreau envelope and provides the associated proofs. |
| title | On the Moreau envelope properties of weakly convex functions |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2509.13960 |