Convex envelopes for ray-concave functions

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)2221-2240
Number of pages20
JournalOptimization Letters
Issue number8
StatePublished - Nov 2022
Externally publishedYes


  • Convex envelopes
  • Convex optimization
  • Nonlinear programming


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