Abstract
Consideration was given to the methods of optimal correction of the improper problems of convex programming based on the Lagrange function regularized in both variables. The methods are independent of the kind of impropriety of the original problem. Approximation precision was estimated, and the relation of this approach to the existing methods of regularization of the incorrect extremal problems was discussed.
Similar content being viewed by others
References
Eremin, I.I., Mazurov, V.D., and Astaf’ev, N.N., Nesobstvennye zadachi lineinogo i vypuklogo programmirovaniya (Improper Problems of Linear and Convex Programming), Moscow: Nauka, 1983.
Skarin, V.D., On the Regularization Method for Contradictory Convex Programming Problems, Izv. Vyssh. Uchebn. Zaved., Mat., 1995, no. 12, pp. 81–88.
Popov, L.D., Using the Modified Prox-method for Optimal Correction of the Improper Problems of Convex Programming, Tr. Inst. Mat. Mekh. UrO RAN, 1995, vol. 3, pp. 261–266.
Vasil’ev, F.P., Metody resheniya ekstremal’nykh zadach (Methods for Solution of Extremal Problems), Moscow: Nauka, 1981.
Gol’shtein, E.G., Teoriya dvoistvennosti v matematicheskom programmirovanii i ee prilozheniya (Duality Theory in Mathematical Programming and its Applications), Moscow: Nauka, 1971.
Tikhonov, A.N. and Arsenin, V.Ya., Metody resheniya nekorrektnykh zadach (Methods for Solving Incorrect Problems), Moscow: Nauka, 1979.
Skarin, V.D., Regularized Lagrange Function and Correction Methods for Improper Convex Programming Problems, in Proc. Steklov Inst. Math. Suppl. 1, 2002, pp. S116–S144.
Author information
Authors and Affiliations
Additional information
Original Russian Text © V.D. Skarin, 2012, published in Avtomatika i Telemekhanika, 2012, No. 2, pp. 99–110.
Rights and permissions
About this article
Cite this article
Skarin, V.D. On some universal methods of correction of the improper convex programming problems. Autom Remote Control 73, 300–309 (2012). https://doi.org/10.1134/S0005117912020087
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117912020087