TY - JOUR
T1 - Nonconvex integration using ϵ-subdifferentials
AU - Correa, Rafael
AU - García, Yboon
AU - Hantoute, Abderrahim
PY - 2018/12/2
Y1 - 2018/12/2
N2 - 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.
AB - 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.
KW - Integration of nonconvex functions
KW - lower semicontinuous convex envelopes
KW - ϵ-subdifferentials
KW - Integration of nonconvex functions
KW - lower semicontinuous convex envelopes
KW - ϵ-subdifferentials
UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85054505360&origin=inward
U2 - 10.1080/02331934.2018.1524471
DO - 10.1080/02331934.2018.1524471
M3 - Article in a journal
SN - 0233-1934
VL - 67
SP - 2205
EP - 2227
JO - Optimization
JF - Optimization
IS - 12
ER -