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The Maximum Principle [2,13] is a well known necessary condition for optimality. This condition, generally, is not sufficient. In [3], the author proved that if there exists regular synthesis  of trajectories, the Maximum Principle also is a sufficient  condition for time-optimality. In this article, we generalize this result for Lagrange, Mayer, and Bolza optimization problems

Sufficient conditions for Lagrange, Mayer, and Bolza optimization problems