Separation of convex cones and extremal problems.

In 1958, the author proved the maximum principle. Pshenichni had written that the proof was sensational, using topology to obtain a result of variational calculus. Later the author worked out the tent method [Boltyanski, V., 1975, Uspehi Mathematika Nauk , 30 , 3-65.] as a general way to solve extremal problems. In fact, main ideas of the method were contained in [Boltyanski, V.G., 1958, Doklady Akademii Nauk SSSR , 119 (6), 1070-1073.]. We give here a short survey of the tent method and the idea of the proof of the maximum principle. [ABSTRACT FROM AUTHOR]