Nonconvex integration using ϵ-subdifferentials. (2nd December 2018)

• Record Type: Journal Article
• Authors: Correa, Rafael; García, Yboon; Hantoute, Abderrahim
• Is Part Of: Optimization. Volume 67:Number 12(2018)
• Page Start: 2205
• Page End: 2227
• Publication Date: 2018-12-02
• Subjects: Integration of nonconvex functions -- ϵ-subdifferentials -- lower semicontinuous convex envelopes; 26B05 -- 26J25 -- 49H05; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1524471
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: 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 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.