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Extragradient Method for Correction of Inconsistent Linear Programming Problems

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Abstract

For a pair of dual inconsistent linear programming problems, the existence and uniqueness of a correction vector that is optimal in the norm is proved. It is shown that the correction problem is reduced to the problem of finding a saddle point of a regularized Lagrange function. A modified extragradient method is proposed for solving the latter problem, and its convergence is proved.

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ACKNOWLEDGMENTS

This work was supported by the Russian Science Foundation, project no. 14-11-00539.

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Correspondence to L. A. Artem’eva, F. P. Vasil’ev or M. M. Potapov.

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Translated by I. Ruzanova

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Artem’eva, L.A., Vasil’ev, F.P. & Potapov, M.M. Extragradient Method for Correction of Inconsistent Linear Programming Problems. Comput. Math. and Math. Phys. 58, 1919–1925 (2018). https://doi.org/10.1134/S0965542518120163

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