ABSTRACT
Functional analysis is the mathematical apparatus on which the construction of the theory of necessary conditions for minimization problems is based. As a matter of fact, only a few basic concepts and a few theorems are used to construct the theory. These concepts are, first of all, the ideas of weak convergence, compactness, and a separation theorem for convex sets. For the reader’s convenience, we shall briefly, and without proofs, state those basic facts of Functional Analysis which are necessary for an understanding of the subsequent material. We shall take them from [1]. Incidentally, the majority of the theorems stated in the sequel – with the exception of a few basic ones – are immediate consequences of the definitions, and may be proved by the reader himself, if he wishes to test whether he correctly understands the introduced definitions.
