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Duality and Correction of Inconsistent Constraints for Improper Linear Programming Problems

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Abstract

We continue the study of approximation properties of alternative duality schemes for improper problems of linear programming. The schemes are based on the use of the classical Lagrange function regularized simultaneously in primal and dual variables. The earlier results on the connection of its saddle points with the lexicographic correction of the right-hand sides of constraints in improper problems of the first and second kind are transferred to a more general type of improperness. Convergence theorems are presented and an informal interpretation of the obtained generalized solution is given.

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Authors and Affiliations

  1. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620990, Russia

    L. D. Popov & V. D. Skarin

  2. Ural Federal University, Yekaterinburg, 620000, Russia

    L. D. Popov & V. D. Skarin

Authors
  1. L. D. Popov
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  2. V. D. Skarin
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Correspondence to L. D. Popov.

Additional information

Original Russian Text © L.D. Popov, V.D. Skarin, 2016, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2016, Vol. 22, No. 3.

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Popov, L.D., Skarin, V.D. Duality and Correction of Inconsistent Constraints for Improper Linear Programming Problems. Proc. Steklov Inst. Math. 299 (Suppl 1), 165–176 (2017). https://doi.org/10.1134/S008154381709019X

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  • DOI: https://doi.org/10.1134/S008154381709019X

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