English

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

Classical Analysis and ODEs 2023-09-04 v1

Abstract

We provide a sufficient condition for an invertible (locally strongly) convex vector-valued function on RN\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.

Keywords

Cite

@article{arxiv.2309.00450,
  title  = {When is the inverse of an invertible convex function itself convex?},
  author = {Robert Planqué},
  journal= {arXiv preprint arXiv:2309.00450},
  year   = {2023}
}