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 for linear copositive problems have similar structure and properties as that proposed in the works by M. Ramana, L. Tuncel, and H. Wolkowicz, for semidefinite programming.
Highlights
Linear Copositive Programming problems can be considered as linear programs over the convex cone of so-called copositive matrices
One interesting property of the obtained results consists in the fact that the new dual formulations for Linear Copositive Programming are closely related to the dual problems proposed in [24, 25, 27] for Semidefinite Programming (SDP)
The main contribution of the paper consists in developing a new approach to dual formulations in Linear Copositive Programming
Summary
Linear Copositive Programming problems can be considered as linear programs over the convex cone of so-called copositive matrices (i.e. matrices which are positive semi-defined on the nonnegative orthant). In [13, 16], we have applied our approach to problems of Linear Copositive Programming and successfully obtained new explicit CQ-free optimality conditions and strong duality results. One interesting property of the obtained results consists in the fact that the new dual formulations for Linear Copositive Programming are closely related to the dual problems proposed in [24, 25, 27] for SDP. This relation confirms the already known deep connection between copositive and semidefinite problems but, taking into account the impact of the duality results of M.
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