-

 

 

 




Optimization Online





 

Symmetric tensor approximation hierarchies for the completely positive cone

Hongbo Dong (hdong6***at***wisc.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.

Download: [PDF]

Entry Submitted: 11/03/2010
Entry Accepted: 11/04/2010
Entry Last Modified: 01/18/2015

Modify/Update this entry


  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository

 

Submit
Update
Policies
Coordinator's Board
Classification Scheme
Credits
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society