Methods for solving variational problems. II. Sliding regimes

The general formalism of the sufficient conditions of the optimality [1] is spread to the case when there is no minimal in the class of permissible functions. Peculiarities of minimizing sequences (sliding optimum regimes) are analyzed. Different methods of determination of these regimes permitting to completely solve the problem are proposed. As a quite possible working hypothesis there is formulated the necessary and, sufficient condition of the optimality – the optimality principle.