The mechanism for the generalized dual problem of network programming solving

Abstract

Abstract The generalized dual problem (GDP) is formulated as a search task of the upper bound minimum (lower bound maximum) for the optimum obtained by solving discrete linear and nonlinear problems by the network programming method. The need for GDP solution arises when, in order to meet the applicability conditions of the method, the right side of the constraint is divided into several unknown summands. The GDP consists in finding of such a partition that ensures achievement of corresponding minimum (maximum). There is no evidence for an existence of the GDP solution for today. However, the conditions for the GDP optimum solution have been formulated. The article proposes an iterative mechanism for search solution of the generalized dual problem. This mechanism is based on the software implementation of the procedure for solving the optimization problem by means of network programming. The application of the mechanism is illustrated on the developing competences task of IT services users. It was shown that the GDP solution exists and is not the only one.