The difficulties associated with the characterization of points of conditional extremum are well known in the case where the restrictions are not independent. In this note we will state a necessary and sufficient condition which takes into account, on the one hand, the method of Milyutin , and on the other hand, the results of , . We only consider the finite-dimensional situation, where the essence of the problem is not overshadowed by details of a functional analytic character. The author is grateful to A.V. Arutyunov for calling his attention to the fact that it would be interesting to obtain a condition for conditional extremum.
Title: One more condition for a conditional extremum
Authors: A.A. Agrachev
Journal title: Uspekhi Matem. Nauk