A note on strict complementarity for the doubly non-negative cone
Bolor Jargalsaikhan, Jan-J. Rückmann · Optimization · 2018
In this paper, we consider a closed convex cone K given by the intersection of two cones K1 and K2. We study faces and complementary faces of K in terms of K1 and K2. Based on complementary faces, the tangent spaces of K 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 cone K. 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.