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A Corrector–Predictor Path-Following Method for Convex Quadratic Symmetric Cone Optimization

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  • Behrouz Kheirfam

    (Azarbaijan Shahid Madani University)

Abstract

After a brief introduction to Euclidean Jordan algebra, we present a new corrector–predictor path-following interior-point algorithm for convex, quadratic, and symmetric cone optimization. In each iteration, the algorithm involves two kind of steps: a predictor (affine-scaling) step and a full Nesterov and Todd (centring) step. Moreover, we derive the complexity for the algorithm, and we obtain the best-known iteration bound for the small-update method.

Suggested Citation

  • Behrouz Kheirfam, 2015. "A Corrector–Predictor Path-Following Method for Convex Quadratic Symmetric Cone Optimization," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 246-260, January.
    • Handle: RePEc:spr:joptap:v:164:y:2015:i:1:d:10.1007_s10957-014-0554-2
    DOI: 10.1007/s10957-014-0554-2
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    References listed on IDEAS

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    1. Shinji Mizuno & Michael J. Todd & Yinyu Ye, 1993. "On Adaptive-Step Primal-Dual Interior-Point Algorithms for Linear Programming," Mathematics of Operations Research, INFORMS, vol. 18(4), pages 964-981, November.
    2. Filiz Gurtuna & Cosmin Petra & Florian Potra & Olena Shevchenko & Adrian Vancea, 2011. "Corrector-predictor methods for sufficient linear complementarity problems," Computational Optimization and Applications, Springer, vol. 48(3), pages 453-485, April.
    3. 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.
    4. S. H. Schmieta & F. Alizadeh, 2001. "Associative and Jordan Algebras, and Polynomial Time Interior-Point Algorithms for Symmetric Cones," Mathematics of Operations Research, INFORMS, vol. 26(3), pages 543-564, August.
    5. G. Q. Wang & Y. Q. Bai, 2012. "A New Full Nesterov–Todd Step Primal–Dual Path-Following Interior-Point Algorithm for Symmetric Optimization," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 966-985, September.
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    Cited by:

    1. Zs. Darvay & T. Illés & B. Kheirfam & P. R. Rigó, 2020. "A corrector–predictor interior-point method with new search direction for linear optimization," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(3), pages 1123-1140, September.

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