Lexicographic regularization and duality for improper linear programming problems / Popov L.D., Skarin V.D. // Proceedings of the Steklov Institute of Mathematics. - 2016. - V. 295, l. . - P. 131-144.

ISSN:
00815438
Type:
Article
Abstract:
A new approach to the optimal lexicographic correction of improper linear programming problems is proposed. The approach is based on the multistep regularization of the classical Lagrange function with respect to primal and dual variables simultaneously. The regularized function can be used as a basis for generating new duality schemes for problems of this kind. Theorems on the convergence and numerical stability of the method are presented, and an informal interpretation of the obtained generalized solution is given. © 2016, Pleiades Publishing, Ltd.
Author keywords:
duality; generalized solutions; improper problems; linear programming; penalty methods; regularization
Index keywords:
нет данных
DOI:
10.1134/S0081543816090145
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https://www.scopus.com/inward/record.uri?eid=2-s2.0-85010468565&doi=10.1134%2fS0081543816090145&partnerID=40&md5=e02898cc8d3ffde3a1c9ad8ef5b5b9a8
Соавторы в МНС:
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Link https://www.scopus.com/inward/record.uri?eid=2-s2.0-85010468565&doi=10.1134%2fS0081543816090145&partnerID=40&md5=e02898cc8d3ffde3a1c9ad8ef5b5b9a8
Affiliations Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, Russian Federation; Ural Federal University, Yekaterinburg, Russian Federation
Author Keywords duality; generalized solutions; improper problems; linear programming; penalty methods; regularization
References Eremin, I.I., Duality for improper problems of linear and convex programming (1981) Soviet Math. Dokl., 23, pp. 62-66; Eremin, I.I., Mazurov, V.D., Astaf’ev, N.N., (1983) Improper Problems of Linear and Convex Programming, , Nauka, Moscow; Eremin, I.I., (2001) Duality in Linear Optimization; Tikhonov, A.N., Arsenin, V.Y., (1981) Solutions of Ill-Posed Problems, , Nauka, Moscow; Vasil’ev, F.P., (1981) Methods for Solving Extremal Problems, , Nauka, Moscow; Skarin, V.D., An approach to the analysis of improper linear programming problems (1986) USSR Comp. Math. Math. Phys., 26 (2), pp. 73-79; Popov, L.D., Linear correction of ill-posed convexly concave minimax problems using the maximin criterion (1986) USSR Comp. Math. Math. Phys., 26 (5), pp. 30-39; Skarin, V.D., On a regularization method for inconsistent convex programming problems (1995) Russ. Math. (Iz. VUZ), 39 (12), pp. 78-85; Gol’shtein, E.G., (1971) Duality Theory in Mathematical Programming and Its Applications, , Nauka, Moscow; Eremin, I.I., Problems in sequential programming (1973) Sib. Math. J., 14 (1), pp. 36-43; Fedorov, V.V., (1979) Numerical Maximin Methods, , Nauka, Moscow; Guddat, J., Stability in convex quadratic parametric programming (1976) Math. Operationsforsch. Statist., 7 (2), pp. 223-245; Dorn, W.S., Duality in quadratic programming (1960) Quart. Appl. Math., 18, pp. 155-162; Hoffman, A.J., On approximate solutions of systems of linear inequalities (1952) J. Res. Nat. Bur. Standards, 49, pp. 263-265
Correspondence Address Popov, L.D.; Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of SciencesRussian 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