Sequential decomposition in optimization problems

A scheme is described in the framework of which tools used in solution of integer and multi-extremum optimization problems are systematized and formalized. The scheme is applied to a group of branch-and-bound methods and a group dynamic programming methods. It can be regarded as a specific case of a general scheme of sequential analysis of versions. A class of problems is outlined to which the scheme is essentially applicable, the main condition being that the feasibility set be representable as a union of a finite number of subsets for each of which a method of solving the problem is known. This extension of the class of problems make the system applicable to functional as well as finite-dimensional optimization problems.