Face reduction and the immobile indices approaches to regularization of linear Copositive Programming problems

TL;DR

This paper introduces two new regularization algorithms for linear Copositive Programming problems based on immobile indices, improving the explicitness and detail of existing methods.

Contribution

It presents novel regularization algorithms utilizing immobile indices, tailored specifically for linear Copositive Programming, enhancing the existing facial reduction approaches.

Findings

Algorithms satisfy Slater condition and strong duality

Immobile-index approach yields more explicit regularization methods

Compared favorably to general convex problem regularization procedures

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 the strong duality holds. We describe here two regularization algorithms based on the concept of immobile indices and an understanding of the important role 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.