On Parametric Copositive Programming Problems

We consider a class of one-parametric copositive programming problems. The aim of the paper is to describe the behavior of solutions to these parametric problems under small parameter perturbations. To do this, we explore the properties of the unperturbed copositive programming problem and show that, under some assumptions, it is closely related to a special type of block semi-infinite programming problem. Taking into account this relationship and the known results on properties of the complementary set of the copositive cone, we obtain a system of a finite number of bi-linear and linear equations with respect to a finite number of variables and a parameter. Under the assumptions made, for any parameter value from a neighborhood of unperturbed parameter value, the system has a unique solution, which allows us to construct optimal primal and dual solutions to the corresponding parametric copositive programming problem.