A note on strict complementarity for the doubly non-negative cone. (4th March 2019) - Jargalsaikhan, Bolor; Rückmann, Jan-J.
ABSTRACT: In this paper, we consider a closed convex coneK given by the intersection of two conesK 1 andK 2 . We study faces and complementary faces ofK in terms ofK 1 andK 2 . Based on complementary faces, the tangent spaces ofK can be characterized as well. Moreover, many numerical methods assume regularity conditions such as strict complementarity. We provide necessary and sufficient conditions for strict complementarity for the coneK . All these results can be applied to the doubly non-negative cone. Finally, a numerically efficient procedure for checking strict complementarity of( X, Y ) for the doubly non-negative cone is provided when X has exactly one zero eigenvalue.