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Integration formulas via the Legendre-Fenchel Subdifferential of nonconvex functions

Rafael Correa(rcorrea***at***dim.uchile.cl)
Garcia Yboon(yboon***at***imca.edu.pe)
Abderrahim Hantoute(ahantoute***at***dim.uchile.cl)

Abstract: Starting from explicit expressions for the subdifferential of the conjugate function, we establish in the Banach space setting some integration results for the so-called epi-pointed functions. These results use the epsilon-subdifferential and the Legendre-Fenchel subdefferential of an appropriate weak lower semicontinuous (lsc) envelope of the initial function. We apply these integration results to the construction of the lsc convex envelope either in terms of the epsilon-subdifferential of the nominal function or of the subdifferential of its weak lsc envelope.

Keywords: integration, lower semicontinuous convex envelope, epi-pointed functions, epsilon-subdifferential, conjugate function

Category 1: Convex and Nonsmooth Optimization

Citation: Will appear in Nonlinear Analysis, Theory and Methods 2011

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Entry Submitted: 05/31/2011
Entry Accepted: 05/31/2011
Entry Last Modified: 05/31/2011

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