Interior penalty functions and duality in linear programming / Eremin I.I., Popov L.D. // Proceedings of the Steklov Institute of Mathematics. - 2013. - V. 283, l. 1. - P. 56-63.

ISSN:

00815438

Type:

Article

Abstract:

Logarithmic additive terms of barrier type with a penalty parameter are included in the Lagrange function of a linear programming problem. As a result, the problem of searching for saddle points of the modified Lagrangian becomes unconstrained (the saddle point is sought with respect to the whole space of primal and dual variables). Theorems on the asymptotic convergence to the desired solution and analogs of the duality theorems for the arising optimization minimax and maximin problems are formulated. © 2013 Pleiades Publishing, Ltd.

Author keywords:

duality; inner penalty functions; linear programming

Index keywords:

нет данных

DOI:

10.1134/S0081543813090058

Смотреть в Scopus:

https://www.scopus.com/inward/record.uri?eid=2-s2.0-84887605423&doi=10.1134%2fS0081543813090058&partnerID=40&md5=c28cedb1522582297c36a3ff4d187d32

Соавторы в МНС:

—

Другие поля

Поле	Значение
Link	https://www.scopus.com/inward/record.uri?eid=2-s2.0-84887605423&doi=10.1134%2fS0081543813090058&partnerID=40&md5=c28cedb1522582297c36a3ff4d187d32
Affiliations	Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990, Russian Federation; Institute of Mathematics and Computer Science, Ural Federal University, pr. Lenina 51, Yekaterinburg, 620000, Russian Federation
Author Keywords	duality; inner penalty functions; linear programming
References	Eremin, I.I., (2002) Theory of Linear Optimization, , Utrecht: VSP; Eremin, I.I., Astaf'ev, N.N., (1976) Introduction to the Theory of Linear and Convex Programming, , Moscow: Nauka; Zangwill, W.I., (1969) Nonlinear Programming: A Unified Approach, , Englewood Cliffs, NJ: Prentice-Hall; Vasil'ev, F.P., (1988) Numerical Methods for Solving Extremal Problems, , Moscow: Nauka; Evtushenko, Y.G., (1982) Methods for Solving Extremal Problems and Their Application in Optimization Systems, , Moscow: Nauka; Elster, K.-H., Reinhardt, R., Schauble, M., Donath, G., (1977) Einfuhrung in Die Nichtlineare Optimierung, , Leipzig: Teubner; Fiacco, A.V., McCormick, G.P., (1968) Nonlinear Programming: Sequential Unconstrained Minimization Techniques, , New York: Wiley; Skarin, V.D., Barrier function method and correction algorithms for improper convex programming problems (2008) Proc. Steklov Inst. Math., Suppl. 2, pp. S120-S134; Roos, C., Terlaky, T., Vial, J.-P., (1997) Theory and Algorithms for Linear Optimization, , Chichester: Wiley
Correspondence Address	Popov, L. D.; Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990, Russian Federation; email: popld@imm.uran.ru
Language of Original Document	English
Abbreviated Source Title	Proc. Steklov Inst. Math.
Source	Scopus