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A Variant of the Simplex Method for Second-Order Cone Programming

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Mathematical Optimization Theory and Operations Research (MOTOR 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11548))

Abstract

The linear second-order cone programming problem is considered. For its solution a variant of the primal simplex-type method is proposed. This variant is a generalization on the cone programming of the standard simplex method for linear programming. At each iteration the dual variable and dual slack are defined, and the move from the given extreme point to another one is realized. Finite and infinite convergence of the method to the solution of the problem having a special form is discussed.

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

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Authors and Affiliations

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

    Vitaly Zhadan

  2. Moscow Institute of Physics and Technology (State Research University), 9 Institutskiy per., Dolgoprudny, Moscow Region, 141701, Russia

    Vitaly Zhadan

Authors
  1. Vitaly Zhadan
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Correspondence to Vitaly Zhadan .

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Editors and Affiliations

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

    Michael Khachay

  2. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Yury Kochetov

  3. University of Florida, Gainesville, FL, USA

    Panos Pardalos

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Zhadan, V. (2019). A Variant of the Simplex Method for Second-Order Cone Programming. In: Khachay, M., Kochetov, Y., Pardalos, P. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2019. Lecture Notes in Computer Science(), vol 11548. Springer, Cham. https://doi.org/10.1007/978-3-030-22629-9_9

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  • DOI: https://doi.org/10.1007/978-3-030-22629-9_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-22628-2

  • Online ISBN: 978-3-030-22629-9

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