Convex envelopes for ray-concave functions

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Resumen

Convexification based on convex envelopes is ubiquitous in the non-linear optimization literature. Thanks to considerable efforts of the optimization community for decades, we are able to compute the convex envelopes of a considerable number of functions that appear in practice, and thus obtain tight and tractable approximations to challenging problems. We contribute to this line of work by considering a family of functions that, to the best of our knowledge, has not been considered before in the literature. We call this family ray-concave functions. We show sufficient conditions that allow us to easily compute closed-form expressions for the convex envelope of ray-concave functions over arbitrary polytopes. With these tools, we are able to provide new perspectives to previously known convex envelopes and derive a previously unknown convex envelope for a function that arises in probability contexts.

Idioma originalInglés
Páginas (desde-hasta)2221-2240
Número de páginas20
PublicaciónOptimization Letters
Volumen16
N.º8
DOI
EstadoPublicada - nov. 2022
Publicado de forma externa

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