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A linear parametrical programming approach for studying and solving bilinear programming problem. (English) Zbl 1131.65051
The authors propose an approach for studying and solving a bilinear programming problem based on linear parametrical programming. Using the duality principle for the considered problem they 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. The algorithm is used for finding the exact solution of the bilinear programming problem as well as its approximate solution.
65K05 Numerical mathematical programming methods
90C05 Linear programming