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

  • Vitaly ZhadanEmail author
Conference paper
  • 195 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12095)

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.

Keywords

Linear second-order cone programming Dual Newton’s method Local convergence Super-linear rate of convergence 

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Dorodnicyn Computing Centre, FRC “Computer Science and Control” of RASMoscowRussia
  2. 2.Moscow Institute of Physics and Technology (State Research University)DolgoprudnyRussia

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