
Journal of Convex Analysis 23 (2016), No. 2, 511530 Copyright Heldermann Verlag 2016 Integration of Nonconvex EpiPointed Functions in Locally Convex Spaces Rafael Correa Centro de Modelamiento Matemático, Universidad de Chile, Beauchef 851, Edificio Norte  Piso 7, Santiago, Chile rcorrea@dim.uchile.cl Abderrahim Hantoute Centro de Modelamiento Matemático, Universidad de Chile, Beauchef 851, Edificio Norte  Piso 7, Santiago, Chile ahantoute@dim.uchile.cl David Salas IMAG, Université Montpellier II, Case Courrier 051, Place Eugčne Bataillon, 34095 Montpellier cedex 05, France david.salas@math.univmonp2.fr We extend results of R. Correa, Y. Garcia and A. Hantoute ["Integration formulas via the (Fenchel) subdifferential of nonconvex functions", Nonlinear Analysis 75(3) (2012) 11881201)] dealing with the integration of nonconvex epipointed functions using the Fenchel subdifferential. In this line, we prove that the classical formula of Rockafellar in the convex setting is still valid in general locally convex spaces for an appropriate family of nonconvex epipointed functions, namely those we call SDPD. The current integration formulas use the Fenchel subdifferential of the involved functions to compare the corresponding closed convex envelopes. Some examples of SDPD functions are investigated. This analysis leads us to approach a useful family of locally convex spaces, referred to as the SDPD, having an RNPlike property. [ Fulltextpdf (194 KB)] for subscribers only. 