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Journal of Optimization Theory and Applications

, Volume 158, Issue 3, pp 816–858 | Cite as

A Full Nesterov–Todd Step Infeasible Interior-Point Method for Second-Order Cone Optimization

  • M. Zangiabadi
  • G. Gu
  • C. Roos
Article

Abstract

After a brief introduction to Jordan algebras, we present a primal–dual interior-point algorithm for second-order conic optimization that uses full Nesterov–Todd steps; no line searches are required. The number of iterations of the algorithm coincides with the currently best iteration bound for second-order conic optimization. We also generalize an infeasible interior-point method for linear optimization to second-order conic optimization. As usual for infeasible interior-point methods, the starting point depends on a positive number. The algorithm either finds a solution in a finite number of iterations or determines that the primal–dual problem pair has no optimal solution with vanishing duality gap.

Keywords

Feasible interior-point method Infeasible interior-point method Second-order conic optimization Jordan algebra Polynomial complexity 

Notes

Acknowledgements

Authors wish to thank Professor Florian Potra and four anonymous referees for useful comments and suggestions on an earlier draft of the manuscript. The first author would like to thank for the financial grant from Shahrekord University. The first author was also partially supported by the Center of Excellence for Mathematics, University of Shahrekord, Shahrekord, Iran.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Applied Mathematics, Faculty of Mathematical SciencesShahrekord UniversityShahrekordIran
  2. 2.Department of MathematicsNanjing UniversityNanjingChina
  3. 3.Department of Electrical Engineering, Mathematics and Computer ScienceDelft University of TechnologyDelftThe Netherlands

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