Separation of convex cones and extremal problems

Abstract

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.

Keywords:

• Optimization
• Variational calculus
• Maximum principle