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arXiv · 2309.00450

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

Robert Planqué
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Abstract

We provide a sufficient condition for an invertible (locally strongly) convex vector-valued function on $\mathbb{R}^N$ 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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Robert Planqué. 2023-09-01. When is the inverse of an invertible convex function itself convex?. https://arxiv.org/abs/2309.00450

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