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International Conference on Optimization and Applications

OPTIMA 2018: Optimization and Applications pp 79–94Cite as

Primal-Dual Newton’s Method with Steepest Descent for Linear Programming

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 974))

Abstract

The primal-dual method for solving linear programming problems is considered. In order to determine the search directions the non-perturbed system of optimality conditions is solved by Newton’s method. If this system is degenerate, then an auxiliary linear complementarity problem is solved for obtained unique directions. Starting points and all consequent points are feasible. The step-lengths are chosen from the steepest descent approach based on minimization of the dual gap. The safety factor is not introduced, and trajectories are allowed to move along the boundaries of the feasible sets. The convergence of the method at a finite number of iterations is proved.

This work was supported by the Russian Foundation for Basic Research (project no. 17-07-00510).

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Author information

Authors and Affiliations

  1. Dorodnicyn Computing Centre, FRC “Computer Science and Control” of RAS, Vaviliva st., 40, 119333, Moscow, Russia

    Vitaly Zhadan

Authors
  1. Vitaly Zhadan
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Correspondence to Vitaly Zhadan .

Editor information

Editors and Affiliations

  1. FRC CSC RAS, Dorodnitsyn Computing Centre, Moscow, Russia

    Yury Evtushenko

  2. University of Montenegro, Podgorica, Montenegro

    Milojica Jaćimović

  3. Krasovsky Institute of Mathematics and Mechanics, Yekaterinburg, Russia

    Michael Khachay

  4. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

    Yury Kochetov

  5. FRC CSC RAS, Dorodnitsyn Computing Centre, Moscow, Russia

    Vlasta Malkova

  6. FRC CSC RAS, Dorodnitsyn Computing Centre, Moscow, Russia

    Mikhail Posypkin

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Zhadan, V. (2019). Primal-Dual Newton’s Method with Steepest Descent for Linear Programming. In: Evtushenko, Y., Jaćimović, M., Khachay, M., Kochetov, Y., Malkova, V., Posypkin, M. (eds) Optimization and Applications. OPTIMA 2018. Communications in Computer and Information Science, vol 974. Springer, Cham. https://doi.org/10.1007/978-3-030-10934-9_6

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  • DOI: https://doi.org/10.1007/978-3-030-10934-9_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-10933-2

  • Online ISBN: 978-3-030-10934-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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