Modified Lagrangians in convex programming and their generalizations (original) (raw)

Abstract

In this paper a rather general class of modified Lagrangians is described for which the main results of the duality theory hold. Within this class two families of modified Lagrangians are taken into special consideration. The elements of the first family are characterized by so-called stability of saddle points and the elements of the second family generate smooth dual problems. The computational methods naturally connected with each of these two families are examined. Further a more general scheme is considered which exploits the idea of modification with respect to the problem of finding a root of a monotone operator. This scheme yields a unified approach to convex programming problems and to determination of saddle and equilibrium points as well as expands the class of modified Lagrangians.

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Authors and Affiliations

  1. Central Economics-Mathematical Institute, Moscow, USSR
    E. G. Gol’shtein & N. V. Tret’yakov

Authors

  1. E. G. Gol’shtein
  2. N. V. Tret’yakov

Editor information

P. Huard

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© 1979 The Mathematical Programming Society

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Gol’shtein, E.G., Tret’yakov, N.V. (1979). Modified Lagrangians in convex programming and their generalizations. In: Huard, P. (eds) Point-to-Set Maps and Mathematical Programming. Mathematical Programming Studies, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120845

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