We develop a mathematical technique of Young dual variational inequalities, which are used to model market equilibrium in a network of production clusters that are heterogeneous from a technological point of view. Two formulations of the problem are considered: for a closed system with a given constraint on resources and for an open system in which resources can be supplied from outside at given prices. A theorem is proved on the existence of a solution to the variational inequality corresponding to market equilibrium in an open system.
Keywords: production network, heterogeneity, variational inequality, Young duality, market equilibrium, resource allocation problem
Received May 11, 2023
Revised June 19, 2023
Accepted June 26, 2023
Funding Agency: This work was supported by the Russian Science Foundation (project no. 23-21-00429, https://rscf.ru/project/23-21-00429/).
Nataliia Obrosova, Cand. Sci. (Phys.-Math.), Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Moscow, 119333 Russia, e-mail: nobrosova@ya.ru
Alexander Shananin, Dr. Phys.-Math. Sci., Prof., RAS Academician, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Moscow, 119333 Russia, e-mail: alexshan@ya.ru
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Cite this article as: N.K. Obrosova, A.A. Shananin. Young duality of variational inequalities. An application for the analysis of interactions in production networks. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2023, vol. 29, no. 3, pp. 88–105; Proceedings of the Steklov Institute of Mathematics (Suppl.), 2023, Vol. 323, Suppl. 1, pp. S194–S210.
