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

Author

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  • M. Zangiabadi

    (Shahrekord University)

  • G. Gu

    (Nanjing University)

  • C. Roos

    (Delft University of Technology)

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.

Suggested Citation

  • M. Zangiabadi & G. Gu & C. Roos, 2013. "A Full Nesterov–Todd Step Infeasible Interior-Point Method for Second-Order Cone Optimization," Journal of Optimization Theory and Applications, Springer, vol. 158(3), pages 816-858, September.
    • Handle: RePEc:spr:joptap:v:158:y:2013:i:3:d:10.1007_s10957-013-0278-8
    DOI: 10.1007/s10957-013-0278-8
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    References listed on IDEAS

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    1. Shinji Mizuno & Michael J. Todd & Yinyu Ye, 1995. "A Surface of Analytic Centers and Primal-Dual Infeasible-Interior-Point Algorithms for Linear Programming," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 135-162, February.
    2. Yu. E. Nesterov & M. J. Todd, 1997. "Self-Scaled Barriers and Interior-Point Methods for Convex Programming," Mathematics of Operations Research, INFORMS, vol. 22(1), pages 1-42, February.
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    Cited by:

    1. M. Sayadi Shahraki & H. Mansouri & M. Zangiabadi, 2017. "Two wide neighborhood interior-point methods for symmetric cone optimization," Computational Optimization and Applications, Springer, vol. 68(1), pages 29-55, September.

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