Symmetric tensor approximation hierarchies for the completely positive cone
Hongbo Dong (hdong6wisc.edu)
Abstract: In this paper we construct two approximation hierarchies for the completely positive cone based on symmetric tensors. We show that one hierarchy corresponds to dual cones of a known polyhedral approximation hierarchy for the copositive cone, and the other hierarchy corresponds to dual cones of a known semidefinite approximation hierarchy for the copositive cone. As an application, we consider a class of bounds on the stability number of a graph obtained from the polyhedral approximation hierarchy, and we construct a primal optimal solution with its tensor lifting for each such linear program.
Keywords: Convex cone, Relaxation, Completely Positive cone, Copositive cone, Tensor
Category 1: Convex and Nonsmooth Optimization (Convex Optimization )
Category 2: Linear, Cone and Semidefinite Programming
Citation: SIAM J. Optim., 23(3), 1850–1866.
Entry Submitted: 11/03/2010
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