Journal of Convex Analysis 31 (2024), No. 3, 847--852
Copyright Heldermann Verlag 2024
When is the Inverse of an Invertible Convex Function Itself Convex?
Robert Planqué
Department of Mathematics, Vrije Universiteit, Amsterdam, The Netherlands
r.planque@vu.nl
We provide a sufficient condition for an invertible (locally strongly) convex vector-valued function on RN 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: Invertible convex function, strongly convex function.
MSC: 26B25.
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