The method of tents in the theory of extremal problems

The method of tents is a unified method of solving various kinds of extremal problems. It is a development of the method of Milyutin and Dubovitskii, but it removes their restrictive assumption that certain cones must be solid. The present exposition is limited to the finite-dimensional case. As applications, we give detailed proofs of very general necessary conditions for various types of extremal problems, such as the problems of mathematical programming, of optimal control (in particular, we include a proof of Pontryagin's maximum principle), and of minimax problems.