A note on strict complementarity for the doubly non-negative cone. (4th March 2019)

• Record Type: Journal Article
• Authors: Jargalsaikhan, Bolor; Rückmann, Jan-J.
• Is Part Of: Optimization. Volume 68:Number 2/3(2019)
• Page Start: 457
• Page End: 464
• Publication Date: 2019-03-04
• Subjects: Complementary faces -- strict complementarity -- doubly non-negative cone -- cone programming; 90C22 -- 90C25 -- 90C99 -- 65K05; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1477943
• Languages: English
• ISSNs: 0233-1934

Abstract

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.