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Facially exposed cones are not always nice

Vera Roshchina(vroshchina***at***ballarat.edu.au)

Abstract: We address the conjecture proposed by Gabor Pataki that every facially exposed cone is nice. We show that the conjecture is true in the three-dimensional case, however, there exists a four-dimensional counterexample of a cone that is facially exposed but is not nice.

Keywords: Nice cone, facially exposed cone, Pataki's conjecture

Category 1: Linear, Cone and Semidefinite Programming

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: CRN, University of Ballarat

Download: [PDF]

Entry Submitted: 06/02/2013
Entry Accepted: 06/03/2013
Entry Last Modified: 06/02/2013

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