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Minimum-Euclidean-norm matrix correction for a pair of dual linear programming problems

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Abstract

For a pair of dual (possibly improper) linear programming problems, a family of matrix corrections is studied that ensure the existence of given solutions to these problems. The case of correcting the coefficient matrix and three cases of correcting an augmented coefficient matrix (obtained by adding the right-hand side vector of the primal problem, the right-hand-side vector of the dual problem, or both vectors) are considered. Necessary and sufficient conditions for the existence of a solution to the indicated problems, its uniqueness is proved, and the form of matrices for the solution with a minimum Euclidean norm is presented. Numerical examples are given.

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Authors and Affiliations

  1. Borisoglebsk Branch, Voronezh State University, Borisoglebsk, Voronezh oblast, 397160, Russia

    V. V. Volkov & M. N. Khvostov

  2. Mozhaisky Military Space Academy, St. Petersburg, 197198, Russia

    V. I. Erokhin & A. V. Razumov

  3. Russia State Social University, Moscow, 129226, Russia

    A. S. Krasnikov

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  1. V. V. Volkov
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  2. V. I. Erokhin
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  3. A. S. Krasnikov
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  4. A. V. Razumov
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  5. M. N. Khvostov
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Correspondence to V. V. Volkov.

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Original Russian Text © V.V. Volkov, V.I. Erokhin, A.S. Krasnikov, A.V. Razumov, M.N. Khvostov, 2017, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2017, Vol. 57, No. 11, pp. 1788–1803.

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Volkov, V.V., Erokhin, V.I., Krasnikov, A.S. et al. Minimum-Euclidean-norm matrix correction for a pair of dual linear programming problems. Comput. Math. and Math. Phys. 57, 1757–1770 (2017). https://doi.org/10.1134/S0965542517110148

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