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On Flood Algorithm for Approximate Solution of Smooth Nonlinear Programming Problems with Linear Constraints of Large Dimension
 
PIIS042473880006776-2-1
DOI10.31857/S042473880006776-2
Publication type Article
Status Published
Authors
Elena Volodina 
Occupation: Associate Professor
Affiliation: Moscow Technical University of Communications and Informatics
Address: Moscow, Russian Federation
Veniamin Livchits
Occupation: Principal Scientific Researcher
Affiliation: Federal Research Center "Informatics and Management" of the Russian Academy of Sciences, Russia
Address: Russian Federation
Journal nameEkonomika i matematicheskie metody
EditionVolume 55 Issue 4
Pages78-88
Abstract

The article analyzes researches in the field of formulation of linear and nonlinear transport problems and algorithms for their solution. The scientific works on the optimization of flows in networks are considered, which made a significant contribution to the creation and development of a new economic and mathematical area as a whole and in many respects stimulated the formation of optimization models and their practical use in a number of industries, first of all in the transport. Particular attention is paid to solving the nonlinear programming problem, when the costs at each transport link depend substantially and nonlinearly not only on the link parameters, but also on the total volume and structure of the cargo flow passing through it. That is, the solution of a large-sized nonlinear inhomogeneous transport problem of a network structure is given when setting the initial information about transportation in the form of a large-sized correspondence matrix. An effective method for optimizing the distribution of inhomogeneous flows over a fixed nonlinear transport network is described. Based on the tools of functional analysis, the theorem of validity of using the conditions of potentiality of the optimal plan for traffic flows in the nonlinear case is proved. The proposed two-stage algorithm for optimizing the step-by-step distribution of inhomogeneous flows over fixed nonlinear transport network is discussed, based on the given evidence of the legitimacy of the principle of potentiality of an optimal transportation plan being extended to this case.

 

Keywordsoptimal planning, nonlinear programming, linear constraint, transport problem, correspondence matrix, costs, cargo flow, step-by-step flow distribution, two-stage optimization algorithm.
Received21.10.2019
Publication date16.12.2019
Number of characters27199
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