Principles to construct disjunctive cuts

Abstract

This article focuses on solving the disjunctive problem. Various methods of constructing disjunctive cuts (DC) from the logical limitations on linear inequalities have been presented. A general principle of DC and a principle allowing to strengthen these cuts were established. By virtue of the stated principles, solving the problems of optimization with a great number of limitations can be simplified. Two theorems were formulated and proved. Four examples illustrated various theoretical statements.

The suggested principles and the procedures based on them provide the theoretical background to the elaboration of algorithms intended for software implementation in solving practical problems.