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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.
MSC:
65K05 Numerical mathematical programming methods
90C05 Linear programming
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