The Distance Between the Perturbation of a Convex Function and its $\Gamma$-regularization

Zichang Liu

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arXiv · 2410.19805

The Distance Between the Perturbation of a Convex Function and its $\Gamma$-regularization

Zichang Liu

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Abstract

In the study of a non-convex minimization problem by Lachand-Robert and Peletier, they found that the difference between the compactly supported perturbation $u+\epsilon h$ of a strictly convex function $u$, and the $\Gamma$-regularization of $u+\epsilon h$, is at most $o(\epsilon)$. Here we find that this result is optimal, albeit they expected a much stronger estimate.

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Zichang Liu. 2024-10-16. The Distance Between the Perturbation of a Convex Function and its $\Gamma$-regularization. https://arxiv.org/abs/2410.19805

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