  This paper investigates the necessary optimality conditions for uniformly
overtaking optimal control on infinite horizon in the free end case. %with free
right endpoint. In the papers of S.M.Aseev, A.V.Kryazhimskii, V.M.Veliov,
K.O.Besov there was suggested the boundary condition for equations of the
Pontryagin Maximum Principle. Each optimal process corresponds to a unique
solution satisfying the boundary condition. Following A.Seierstad's idea, in
this paper we prove a more general geometric variety of that boundary
condition. We show that this condition is necessary for uniformly overtaking
optimal control on infinite horizon in the free end case. A number of
assumptions under which this condition selects a unique Lagrange multiplier is
obtained. The results are applicable to general non-stationary systems and the
optimal objective value is not necessarily finite. Some examples are discussed.
