Iterative process of the search for coincidence points in the model ``supply-demand''
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Winter Mathematical School "Modern Methods of Function Theory and Related Problems", Voronezh, January 28 - February 2, 2021, Part 2, Tome 207 (2022), pp. 68-76.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we construct an algorithm for finding equilibrium positions in the “supply-demand” model based on the theory of covering mappings and the problem of coincidence points for two mappings. The search algorithm is based on the Hooke–Jeeves method. A software implementation of the algorithm is verified by numerical experiments for model dimensions $1$$4$.
Keywords: coincidence point, supply, covering mapping, iterative process, economic equilibrium.
Mots-clés : demand
@article{INTO_2022_207_a7,
     author = {A. M. Kotyukov},
     title = {Iterative process of the search for coincidence points in the model ``supply-demand''},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {68--76},
     publisher = {mathdoc},
     volume = {207},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_207_a7/}
}
TY  - JOUR
AU  - A. M. Kotyukov
TI  - Iterative process of the search for coincidence points in the model ``supply-demand''
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2022
SP  - 68
EP  - 76
VL  - 207
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2022_207_a7/
LA  - ru
ID  - INTO_2022_207_a7
ER  - 
%0 Journal Article
%A A. M. Kotyukov
%T Iterative process of the search for coincidence points in the model ``supply-demand''
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2022
%P 68-76
%V 207
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2022_207_a7/
%G ru
%F INTO_2022_207_a7
A. M. Kotyukov. Iterative process of the search for coincidence points in the model ``supply-demand''. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Winter Mathematical School "Modern Methods of Function Theory and Related Problems", Voronezh, January 28 - February 2, 2021, Part 2, Tome 207 (2022), pp. 68-76. http://geodesic.mathdoc.fr/item/INTO_2022_207_a7/

[1] Arutyunov A. V., “Nakryvayuschie otobrazheniya v metricheskikh prostranstvakh i nepodvizhnye tochki”, Dokl. RAN., 416:2 (2007), 151–155 | Zbl

[2] Arutyunov A. V., “Tochki sovpadeniya dvukh otobrazhenii”, Funkts. anal. prilozh., 48:1 (2014), 89–93 | MR | Zbl

[3] Arutyunov A. V., Zhukovskii S. E., Pavlova N. G., “Ravnovesnye tseny kak tochka sovpadeniya dvukh otobrazhenii”, Zh. vychisl. mat. mat. fiz., 53:2 (2013), 225–237 | MR | Zbl

[4] Arrow K. J., Debreu G., “Existence of an equilibrium for a competitive economy”, Econometrica., 22:3 (1954), 265–290 | DOI | MR | Zbl

[5] Arutyunov A. V., Pavlova N. G., Shananin A. A., “New conditions for the existence of equilibrium prices”, Yugoslav. J. Oper. Res., 28:1 (2018), 59–77 | DOI | MR | Zbl

[6] Pavlova N. G., “Applications of the theory of covering maps to the study of dynamic models of economic processes with continuous time”, Mathematical Analysis With Applications, eds. Pinelas S., Kim A., Vlasov V., Springer, Cham, 2020, 123–129 | DOI | MR | Zbl

[7] Pavlova N. G., “Necessary conditions for closedness of the technology set in dynamical Leontief model”, Proc. 11 Int. Conf. “Management of Large-Scale System Development”, 2018, 1–4

[8] Pavlova N., Zhukovskaya Z., Zhukovskiy S., “Equilibrium in continuous dynamic market models”, Proc. 15 Int. Conf. on Stability and Oscillations of Nonlinear Control Systems, 2020, 1–3

[9] Smith A., An Inquiry into the Nature and Cause of the Wealth of Nations, William Strahan and Thomas Cadell, London, 1776

[10] Walras L., Elements d'Economie Politique Pure, Corbaz, Lausanne, 1874