We consider the problem of minimization of the functional with restrictions on a condition x and control u in the form of operational equality and functional inequalities. The space of the control is the KV- lineal with the unit. The article presents the conditions of the ordinal convergence the finite-dimensional regularizating sequence to the set of the optimal controls in the KV- lineal of the limitating elements. This sequence is constructed using the A.N. Tikhonov's method of the regularization
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