Nonconvex integration using ϵ-subdifferentials

Rafael Correa, Yboon García, Abderrahim Hantoute

Research output: Contribution to journalArticle in a journalpeer-review

3 Scopus citations


We give an integration criterion for nonconvex functions defined in locally convex spaces. We prove that an inclusion-type relationship between the ϵ-subdifferentials, for small amount of ϵ > 0 of any two functions is sufficient for the equality of the associated closed convex envelopes, up to an additive constant and to a recession term, that is related to the asymptotic behaviour of the functions. This recession term is dropped out when the functions are convex. We use these results to represent both the values of closed convex envelopes and their ϵ-subdifferentials by means of ϵ-subdifferentials of the original function.
Original languageEnglish
Pages (from-to)2205-2227
Number of pages23
Issue number12
StatePublished - 2 Dec 2018


  • Integration of nonconvex functions
  • lower semicontinuous convex envelopes
  • ϵ-subdifferentials


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