The Distance Between the Perturbation of a Convex Function and its Γ-regularization

2024/10/16 by Zichang Liu, Liu, Zichang
Computer Science · Mathematics · #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #Functional Equations Stability Results #Numerical methods in inverse problems #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2410.19805

openalex publication_date 2024/10/16 · openalex created_date 2024/11/14 · openalex updated_date 2026/07/28

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+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.

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