Abstract
In this paper, we study the properties of faces and exposed faces of the cone of copositive matrices (copositive cone), paying special attention to issues related to their geometric structure. Based on the concepts of zero and minimal zero vectors, we obtain several explicit representations of faces of the copositive cone and compare them. Given a face of the cone of copositive matrices, we describe the subspace generated by that face and the minimal exposed face containing it. Summarizing the results obtained in the paper, we systematically show what information can be extracted about the given copositive face in the case of incomplete data. Several examples for illustrating the main findings of the paper and also for justifying the usefulness of the developed approach to the study of the facial structure of the copositive cone are discussed.
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference19 articles.
1. Copositive Programming via Semi-Infinite Optimization
2. Copositive optimization – Recent developments and applications
3. Copositive Programming—A survey;Dür,2010
4. Handbook of Semidefinite, Conic and Polynomial Optimization,2012
5. Handbook of Semidefinite Programming—Theory, Algorithms, and Applications,2000
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