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The Dual Simplex-Type Method for Linear Second-Order Cone Programming Problem

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Optimization and Applications (OPTIMA 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12422))

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Abstract

The linear second-order cone programming problem is considered. For its solution, the dual simplex-type method is proposed. The method is the generalization of the standard dual simplex method for linear programming for cone programming. At each iteration the primal variable is defined, and pivoting of the dual variable is carried out. The proof of the local convergence is given.

This investigation was supported by the Ministry of Science and Higher Education of the Russian Federation, project No. 075-15-2020-799.

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Authors and Affiliations

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

    Vitaly Zhadan

Authors
  1. Vitaly Zhadan
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Correspondence to Vitaly Zhadan .

Editor information

Editors and Affiliations

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

    Nicholas Olenev

  2. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Yuri Evtushenko

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

    Michael Khachay

  4. Dorodnicyn Computing Centre, FRC CSC RAS, Moscow, Russia

    Vlasta Malkova

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Zhadan, V. (2020). The Dual Simplex-Type Method for Linear Second-Order Cone Programming Problem. In: Olenev, N., Evtushenko, Y., Khachay, M., Malkova, V. (eds) Optimization and Applications. OPTIMA 2020. Lecture Notes in Computer Science(), vol 12422. Springer, Cham. https://doi.org/10.1007/978-3-030-62867-3_22

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