Mathematical Problems in Engineering
Volume 7 (2001), Issue 2, Pages 177-203

Sufficient conditions for Lagrange, Mayer, and Bolza optimization problems

V. Boltyanski

CIMAT, A.P. 402, 36000 Guanajuato, GTO, Mexico

Received 7 February 2000

Copyright © 2001 V. Boltyanski. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.