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.

本文致力于研究线性共积规划问题的强对偶性。基于最近引入的归一化固定索引集合的概念，得出了扩展对偶问题。对偶问题满足强对偶关系，并且不需要任何其他正则性假设，例如约束条件。与先前获得的结果的主要区别在于，现在扩展对偶问题既不使用固定索引本身，也不使用有关这些索引的凸包的显式信息。本文提出的针对线性共正问题的强对偶公式具有与M.Ramana，L.Tuncel和H.Wolkowicz在半定规划中提出的结构和性质相似的结构和性质。