Convex envelopes for ray-concave functions

Barrera, Javiera; Moreno, Eduardo; Munoz, Gonzalo

Abstract

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.

Más información

Título según WOS: Convex envelopes for ray-concave functions
Título de la Revista: OPTIMIZATION LETTERS
Volumen: 16
Número: 8
Editorial: SPRINGER HEIDELBERG
Fecha de publicación: 2022
Página de inicio: 2221
Página final: 2240
DOI:

10.1007/s11590-022-01852-2

Notas: ISI