On decomposition of linear functional problems. I. Linear programming in a Hilbertian space

The paper is concerned with search for a feasible solution of a functional linear programming problem (FLPP); a decompsitional approach is proposed in which the FLPP is interpreted as a problem of finding the intersectional point of two convex sets of a certain functional space, and than solved by the method of successing design or its modification. The problem of mapping on one of the sets is decomposed into a specified number of independent subproblems and the one of mapping on another set is solved in a finite form.