A Linear Parametrical Programming Approach for Studying and Solving Bilinear Programming Problem

An approach for studying and solving a bilinear programming problem, based on linear parametrical programming, is proposed. Using duality principle for the considered problem we show that it can be transformed into a problem of determining the compatibility of a system of linear inequalities with a right-hand member that depends on parameters, admissible values of which are defined by another system of linear inequalities. Some properties of this auxiliary problem are obtained and a conical algorithm for its solving is proposed. We show that this algorithm can be used for finding the exact solution of bilinear programming problem as well as its approximate solution.