Regularization Algorithms for Linear Copositive Programming Problems: An Approach Based on the Concept of Immobile Indices

Abstract

In this paper, we continue an earlier study of the regularization procedures of linear copositive problems and present new algorithms that can be considered as modifications of the algorithm described in our previous publication, which is based on the concept of immobile indices. The main steps of the regularization algorithms proposed in this paper are explicitly described and interpreted from the point of view of the facial geometry of the cone of copositive matrices. The results of the paper provide a deeper understanding of the structure of feasible sets of copositive problems and can be useful for developing a duality theory for these problems.