This paper continues studies of non-intersection properties finite collections sets initiated 40 years ago by the extremal principle. We study elementary sets, making core conventional definitions extremality and stationarity. In setting general Banach/Asplund spaces, we establish new primal (slope) dual (generalized separation) necessary conditions for these properties. The results are applied...

A closed convex conic subset [Formula: see text] of the positive semidefinite (PSD) cone is rank-one generated (ROG) if all its extreme rays are by matrices. The ROG property closely related to exactness program (SDP) relaxations nonconvex quadratically constrained quadratic programs (QCQPs) text]. We consider case where obtained as intersection PSD with finitely many homogeneous linear matrix ...