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New formulas for the Fenchel subdifferential of the conjugate function

Abderrahim Hantoute (ahantoute***at***dim.uchile.cl)
Rafael Correa (rcorrea***at***dim.uchile.cl)

Abstract: Following [13] we provide new formulas for the Fenchel subdifferential of the conjugate of functions defined on locally convex spaces. In particular, this allows deriving expressions for the minimizers set of the lower semicontinuous convex hull of such functions. These formulas are written by means of primal objects related to the subdifferential of the initial function, namely a new enlargement of the Fenchel subdifferential operator.

Keywords: Fenchel conjugate and biconjugate, Fenchel subdifferential, Lower semi- continuous convex hull, Argmin sets.

Category 1: Convex and Nonsmooth Optimization

Category 2: Infinite Dimensional Optimization

Citation: Set-valued and Varioational Analysis Volume 18, Numbers 3-4, 405-422

Download: [PDF]

Entry Submitted: 08/27/2010
Entry Accepted: 08/27/2010
Entry Last Modified: 12/16/2010

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