Regularization algorithms for linear copositive problems

Abstract

The paper is devoted to the regularization of linear Copositive Programming problems which consists of transforming a problem to an equivalent form, where the Slater condition is satisfied and therefore the strong duality holds. We describe regularization algorithms based on a concept of immobile indices and on the understanding of the important role that these indices play in the feasible sets' characterization. These algorithms are compared to some regularization procedures developed for a more general case of convex problems and based on a facial reduction approach. We show that the immobile-index-based approach combined with the specifics of copositive problems allows us to construct more explicit and detailed regularization algorithms for linear Copositive Programming problems than those already available.