  An uniform LP duality is an useful property of conic matrix systems. A
consistent linear conic optimization problem yields uniform LP duality if for
any linear cost function, for which the primal problem has finite optimal
value, the corresponding Lagrange dual problem is attainable and the duality
gap vanishes.
  In this paper, we establish new necessary and sufficient conditions
guaranteing the uniform LP duality for linear problems of Copositive
Programming and formulate these conditions in different equivalent forms. The
main results are obtained using an approach developed in previous papers of the
authors and based on a concept of immobile indices that permits alternative
representations of the set of feasible solutions.

Optimization and Control