Abstract
A doublestep extragradient method for solving nonintrinsic problems of linear programming, variational inequalities, and some related problems is presented in the article. The convergence of this method in the general case is proved. The convergence of the method at the rate of geometric progression is proved for the problems of linear programming.
Similar content being viewed by others
References
Eremin, I.I., Mazurov, Vl.D., and Astaf’ev, N.N., Nesobstvennye zadachi lineinogo i vypuklogo programmirovaniya (Improper Problems of Linear and Convex Programming), Moscow: Nauka, 1983.
Eremin, I.I., Protivorechivye modeli optimal’nogo planirovaniya (Inconsistent Models of Optimal Planning), Moscow: Nauka, 1988.
Eremin, I.I., Mazurov, Vl.D., Skarin, V.D., and Khachai, M.Yu., Matematicheskie metody v ekonomike (Mathematical Methods in Economics), Ekaterinburg: Ural. Otd. Ross. Akad. Nauk, 2000.
Korpelevich, G.M., Extragradient Method for Finding of Saddle Points and Other Problems, Ekon. Mat. Metody, 1976, vol. 12, no. 4, pp. 747–756.
Antipin, A.S., Methods of Solution of Variation Inequalities with Bound Restrictions, Zh. Vychisl. Mat. Mat. Fiz., 2000, vol. 40, no. 9, pp. 1291–1307.
Zykina, A.V., Reverse Complementarity in Model of Resource Management, Zh. Vychisl. Mat. Mat. Fiz., 2008, vol. 48, no. 11, pp. 1968–1978.
Dem’yanov, V.F. and Pevnyi, A.B., Digital Methods of Saddle Point Finding, Zh. Vychisl. Mat. Mat. Fiz., 1972, vol. 12, no. 5, pp. 1099–1127.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.V. Zykina, N.V. Melen’chuk, 2010, published in Modelirovanie i Analiz Informatsionnykh Sistem, 2010, No. 1, pp. 65–75.
About this article
Cite this article
Zykina, A.V., Melen’chuk, N.V. A doublestep extragradient method for solving a problem of the management of resources. Aut. Conrol Comp. Sci. 45, 452–459 (2011). https://doi.org/10.3103/S0146411611070170
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0146411611070170