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Dual Newton’s Methods for Linear Second-Order Cone Programming

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Mathematical Optimization Theory and Operations Research (MOTOR 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12095))

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Abstract

The linear second-order cone programming problem is considered. For its solution, two dual Newton’s methods are proposed. These methods are constructed with the help of optimality conditions. The nonlinear system of equations, obtained from the optimality conditions and depended only from dual variables, is solved by the Newton method. Under the assumption that there exist strictly complementary solutions of both primal and dual problems the local convergence of the methods with super-linear rate is proved.

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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

  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. Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russia

    Alexander Kononov

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

    Michael Khachay

  3. National Research University Higher School of Economics, Nizhny Novgorod, Russia

    Valery A Kalyagin

  4. University of Florida, Gainesville, FL, USA

    Panos Pardalos

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Zhadan, V. (2020). Dual Newton’s Methods for Linear Second-Order Cone Programming. In: Kononov, A., Khachay, M., Kalyagin, V., Pardalos, P. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2020. Lecture Notes in Computer Science(), vol 12095. Springer, Cham. https://doi.org/10.1007/978-3-030-49988-4_2

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