Strong duality for a problem of linear copositive programming

TL;DR

This paper establishes strong duality for linear copositive programming problems using a novel dual formulation that avoids regularity assumptions and explicit immobile index information.

Contribution

It introduces an extended dual problem for linear copositive programming that guarantees strong duality without regularity conditions, using new techniques distinct from prior semidefinite programming results.

Findings

The extended dual problem satisfies strong duality relations.

The dual formulation does not require additional regularity assumptions.

It generalizes duality results similar to those in semidefinite programming.

Abstract

The paper is dedicated to the study of strong duality for a problem of linear copositive programming. Based on the recently introduced concept of the set of normalized immobile indices, an extended dual problem is deduced. The dual problem satisfies the strong duality relations and does not require any additional regularity assumptions such as constraint qualifications. The main difference with the previously obtained results consists in the fact that now the extended dual problem uses neither the immobile indices themselves nor the explicit information about the convex hull of these indices. The strong duality formulations presented in the paper have similar structure and properties as that proposed in the works of M. Ramana, L. Tuncel, and H. Wolkovicz, for semidefinite programming, but are obtained using different techniques.