Dual approach to the application of barrier functions for the optimal correction of improper linear programming problems of the first kind / Popov L.D. // Proceedings of the Steklov Institute of Mathematics. - 2015. - V. 288, l. . - P. 173-179.

ISSN:
00815438
Type:
Article
Abstract:
A novel dual approach to the problem of optimal correction of first-kind improper linear programming problems with respect to their right-hand sides is proposed. It is based on the extension of the traditional Lagrangian by introducing additional regularization and barrier components. Convergence theorems are given for methods based on the augmented Lagrangian, an informal interpretation of the obtained generalized solution is suggested, and results of numerical experiments are presented. © 2015, Pleiades Publishing, Ltd.
Author keywords:
barrier function method; generalized solutions; improper problems; linear programming
Index keywords:
нет данных
DOI:
10.1134/S0081543815020170
Смотреть в Scopus:
https://www.scopus.com/inward/record.uri?eid=2-s2.0-84958238098&doi=10.1134%2fS0081543815020170&partnerID=40&md5=f5ad52781f3e39a3ea52f4f160154af2
Соавторы в МНС:
Другие поля
Поле Значение
Link https://www.scopus.com/inward/record.uri?eid=2-s2.0-84958238098&doi=10.1134%2fS0081543815020170&partnerID=40&md5=f5ad52781f3e39a3ea52f4f160154af2
Affiliations Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, Russian Federation; Institute of Mathematics and Computer Science, Ural Federal University, pr. Lenina 51, Yekaterinburg, Russian Federation
Author Keywords barrier function method; generalized solutions; improper problems; linear programming
Funding Details 12-P-1-1016, UB RAS, Russian Foundation for Basic Research; 12-P-1-1023, UB RAS, Russian Foundation for Basic Research; 12-P-1-1034, UB RAS, Russian Foundation for Basic Research; 12-S-1-1017/1, UB RAS, Russian Foundation for Basic Research; 13-01-00210, RFBR, Russian Foundation for Basic Research; 13-07-00181, RFBR, Russian Foundation for Basic Research
References Eremin, I.I., Duality for improper problems of linear and convex programming (1981) Dokl. Akad. Nauk SSSR, 256 (2), pp. 272-276; Eremin, I.I., Mazurov, V.D., Astaf’ev, N.N., (1983) Improper Problems of Linear and Convex Programming, , Nauka, Moscow; Eremin, I.I., (1988) Contradictory Models of Optimal Planning, , Nauka, Moscow; Morozov, V.A., Pseudo-solutions (1969) USSR Comp. Math. Math. Phys., 9 (6), pp. 196-203; Kochikov, I.V., Matvienko, A.N., Yagola, A.G., A generalized discrepancy principle for solving incompatible equations (1984) USSR Comp. Math. Math. Phys., 24 (4), pp. 78-80; Skarin, V.D., Barrier function method and correction algorithms for improper convex programming problems (2008) Proc. Steklov Inst. Math., Suppl. 2, pp. S120-S134; Popov, L.D., Use of barrier functions for optimal correction of improper problems of linear programming of the 1st kind (2012) Autom. Remote Control, 73 (3), pp. 417-424; Eremin, I.I., Astaf’ev, N.N., (1976) Introduction to the Theory of Linear and Convex Programming, , Nauka, Moscow; Fiacco, A.V., McCormick, G.P., (1968) Nonlinear Programming: Sequential Unconstrained Minimization Techniques, , Wiley, New York; Eremin, I.I., Popov, L.D., Interior penalty functions and duality in linear programming (2013) Proc. Steklov Inst. Math., 283, pp. S56-S63
Correspondence Address Popov, L.D.; Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Russian Federation; email: popld@imm.uran.ru
Publisher Maik Nauka-Interperiodica Publishing
Language of Original Document English
Abbreviated Source Title Proc. Steklov Inst. Math.
Source Scopus