Use of barrier functions for optimal correction of improper problems of linear programming of the 1st kind / Popov L.D. // Automation and Remote Control. - 2012. - V. 73, l. 3. - P. 417-424.

ISSN:
00051179
Type:
Article
Abstract:
Possibilities are investigated of the combined use of interior and exterior penalty functions for discovering the generalized (approximate) solutions of improper problems of linear programming of the 1st kind. Diagrams of algorithms, theorems of convergence, results of numerical experiments are presented. © 2012 Pleiades Publishing, Ltd.
Author keywords:
Index keywords:
Barrier functions; Numerical experiments; Optimal correction; Penalty function; Automation; Control; Linear programming
DOI:
10.1134/S0005117912030010
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Affiliations Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russian Federation
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, Vl.D., Astafiev, N.N., (1983) Nesobstvennye Zadachi Lineinogo i Vypuklogo Program-mirovaniya (Improper Problems of Linear and Convex Programmming), , Moscow: Nauka; Eremin, I.I., (1988) Protivorechivye Modeli optimal'Nogo Planirovaniya (Contradictory Models of Optimal Planning), , Moscow: Nauka; Morozov, V.A., On pseudosolutions (1969) Zh. Vychisl. Mat. Mat. Fiz., 9 (6), pp. 1387-1391; Kochikov, I.V., Matvienko, A.N., Yagola, A.G., Generalized principle of the residual for solution of incompatible equations (1984) Zh. Vychisl. Mat. Mat. Fiz., 24 (7), pp. 1087-1090; (1988) Issledovaniya Po Nesobstvennym Zadacham Optimizatsii: Sb. Statei (Investigations on Improper Problems of Optimization: Collection of Works), , Sverdlovsk: UrO Akad. Nauk SSSR; (1985) Parametricheskaya Optimizatsiya i Metody Approksimatsii Nesobstvennykh Zadach Matematicheskogo Pro-grammirovaniya: Sb. Statei (Parametric Optimization and Methods of Approximation of the Improper Problems of Mathematical Programming: Collection of Works), , Sverdlovsk: UNTs Akad. Nauk SSSR; (1990) Neregulyarnaya Dvoistvennost' v Matematicheskom Programmirovanii: Sb. Statei (Irregular Duality in Mathematical Programming: Collextion of Works), , Sverdlovsk: UrO Akad. Nauk SSSR; Popov, L.D., Application of the modified method for optimal correction of improper problems of convex programming (1995) Tr. Inst. Mat. Mekh. Ural. Otd. Ross. Akad. Nauk, 3, pp. 261-266; Popov, L.D., Symmetric systems and fejer processes for improper problems of linear programming (2005) Methods of Optimization and Their Applications: Proc. XIII Intern. Baikal. Sch. Seminar (ISEM so Ross. Akad. Nauk), 1, pp. 141-146. , Irkutsk; Skarin, V.D., On the method of barrier functions and algorithms for correction of improper problems of convex programming (2008) Tr. Inst. Mat. Mekh. Ural. Otd. Ross. Akad. Nauk, 14 (2), pp. 115-128; Fiacco, A.V., McCormick, G.P., (1968) Nonlinear Programming: Sequential Unconstrained Minimization Techniques, , New York: Wiley Translated under the title Nelineinoe programmirovanie. Metody posledovatel'noi bezuslovnoi minimizatsii, Moscow: Mir, 1972; Roos, C., Terlaky, T., Vial, J.-Ph., (1997) Theory and Algorithms for Linear Optimization, , Chichester: Wiley
Correspondence Address Popov, L.D.; Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russian Federation
Language of Original Document English
Abbreviated Source Title Autom. Remote Control
Source Scopus