Global convergence of an inexact interior-point method for convex quadratic‎ ‎symmetric cone programming‎

Authors

  • H. Mansouri Department of Applied Mathematics‎, ‎Faculty of‎ ‎Mathematical Sciences‎, ‎Shahrekord University‎, ‎P.O‎. ‎Box 115‎, ‎Shahrekord‎, ‎Iran.
  • M. Pirhaji Department of Applied Mathematics‎, ‎Faculty of‎ ‎Mathematical Sciences‎, ‎Shahrekord University‎, ‎P.O‎. ‎Box 115‎, ‎Shahrekord‎, ‎Iran.
  • M. Zangiabadi Department of Applied Mathematics‎, ‎Faculty of ‎Mathematical Sciences‎, ‎Shahrekord University‎, ‎P.O‎. ‎Box 115‎, ‎Shahrekord‎, ‎Iran.
Abstract:

‎In this paper‎, ‎we propose a feasible interior-point method for‎ ‎convex quadratic programming over symmetric cones‎. ‎The proposed algorithm relaxes the‎ ‎accuracy requirements in the solution of the Newton equation system‎, ‎by using an inexact Newton direction‎. ‎Furthermore‎, ‎we obtain an‎ ‎acceptable level of error in the inexact algorithm on convex‎ ‎quadratic symmetric cone programming (CQSCP)‎. ‎We also prove that the iteration‎ ‎bound for the feasible short-step method is‎ ‎$O(sqrt{n}logfrac{1}{varepsilon})$‎, ‎and‎ ‎$O(nlogfrac{1}{varepsilon})$ for the large-step method which coincide with the currently best‎ ‎known iteration bounds for CQSCPs.

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Journal title

volume 42  issue 6

pages  1363- 1385

publication date 2016-12-18

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