The Distance Between the Perturbation of a Convex Function and its $Γ$-regularization
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917818178469888 |
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| author | Liu, Zichang |
| author_facet | Liu, Zichang |
| contents | In the study of a non-convex minimization problem by Lachand-Robert and Peletier, they found that the difference between the compactly supported perturbation $u+εh$ of a strictly convex function $u$, and the $Γ$-regularization of $u+εh$, is at most $o(ε)$. Here we find that this result is optimal, albeit they expected a much stronger estimate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19805 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Distance Between the Perturbation of a Convex Function and its $Γ$-regularization Liu, Zichang Optimization and Control Analysis of PDEs Classical Analysis and ODEs Differential Geometry In the study of a non-convex minimization problem by Lachand-Robert and Peletier, they found that the difference between the compactly supported perturbation $u+εh$ of a strictly convex function $u$, and the $Γ$-regularization of $u+εh$, is at most $o(ε)$. Here we find that this result is optimal, albeit they expected a much stronger estimate. |
| title | The Distance Between the Perturbation of a Convex Function and its $Γ$-regularization |
| topic | Optimization and Control Analysis of PDEs Classical Analysis and ODEs Differential Geometry |
| url | https://arxiv.org/abs/2410.19805 |