« On Sufficient and Necessary Conditions for Rank-1 Generatedness Property of Cones
On Sufficient and Necessary Conditions for Rank-1 Generatedness Property of Cones
October 09, 2019, 3:00 PM - 3:45 PM
Location:
Auditorium (Amphitheatre Banque Nationale)
HEC Montreal
Cote-Sainte-Catherine Building
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Fatma Kılınç-Karzan, Carnegie Mellon University
A convex cone $K$ that is a subset of the positive semidefinite (PSD) cone is called rank-one generated (ROG) if all of its extreme rays are generated by rank 1 matrices. ROG property is closely related to the characterizations of exactness of SDP relaxations, e.g., of nonconvex quadratic programs. We consider the case when $K$ is obtained as the intersection of the PSD cone with finitely many linear (or conic) matrix inequalities, and identify sufficient conditions that guarantee that $K$ is ROG. In the case of two linear matrix inequalities, we also establish the necessity of our sufficient condition.
This is joint work with C.J. Argue.