S. Chernov, S. Titov, L. Chernova, N. Kunanets, L. Chernova,

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Abstract. For determining ways of company development, ensuring the growth of profit in manufacture and sales of certain products, it has been proposed to use an algorithm of constructing a problem being inverse to primal-dual one, for minimization of the project costs. The primal and the inverse problems contribute to improving the efficiency of calculation when determining approaches for minimization of costs. This pair of problems is mutually conjugate. The proposed rigorous approach to obtaining the algorithm of constructing a dual problem is based on the following statement: a problem being inverse to a dual one is a primal (original) problem. The authors have proposed and rigorously proven the algorithm of a general approach to the construction of conjugate problem pairs. Formalization of the algorithm developed allows obtaining easily correct pairs of known dual problems. This permitted proposing and proving the truth of the algorithm of constructing a dual problem for the arbitrary form of a primal problem representation.

Keywords: linear optimization, primal problem, dual problem, duality, objective function, constraint system, pairs of dual problems

Determination of Approaches for Project Costs Minimization with Use of Dual Problems

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