Title: One more condition for a conditional extremum
Authors: A.A. Agrachev
Journal title: Uspekhi Matem. Nauk
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.