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VERTICES OF SPECTRAHEDRA ARISING FROM THE ELLIPTOPE, THE THETA BODY, AND THEIR RELATIVES

Marcel K. de Carli Silva(mksilva***at***math.uwaterloo.ca)
Levent Tuncel(ltuncel***at***math.uwaterloo.ca)

Abstract: Utilizing dual descriptions of the normal cone of convex optimization problems in conic form, we characterize the vertices of semidefinite representations arising from Lovász theta body, generalizations of the elliptope, and related convex sets. Our results generalize vertex characterizations due to Laurent and Poljak from the 1990’s. Our approach also leads us to nice characterizations of strict complementarity and to connections with some of the related literature.

Keywords: semidefinite programming, theta body, elliptope, boundary structure of convex sets

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Category 2: Combinatorial Optimization (Other )

Citation: Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, September 2013.

Download: [PDF]

Entry Submitted: 11/28/2013
Entry Accepted: 11/28/2013
Entry Last Modified: 11/28/2013

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