When is the inverse of an invertible convex function itself convex?

2023/09/01 by Robert Planqué, Planqué, Robert
Computer Science · Mathematics · #26B25 #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2309.00450

openalex publication_date 2023/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a sufficient condition for an invertible (locally strongly) convex vector-valued function on ℝ^N to have a (locally strongly) convex inverse. We show under suitable conditions that if the gradient of each component of the inverse has negative entries, then this inverse is (locally strongly) convex if the original is.

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