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Full Nesterov-Todd step infeasible interior-point method for symmetric optimization

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

Abstract

Euclidean Jordan algebras were proved more than a decade ago to be an indispensable tool in the unified study of interior-point methods. By using it, we generalize the full-Newton step infeasible interior-point method for linear optimization of Roos [Roos, C., 2006. A full-Newton step O(n) infeasible interior-point algorithm for linear optimization. SIAM Journal on Optimization. 16 (4), 1110-1136 (electronic)] to symmetric optimization. This unifies the analysis for linear, second-order cone and semidefinite optimizations.

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  • Gu, G. & Zangiabadi, M. & Roos, C., 2011. "Full Nesterov-Todd step infeasible interior-point method for symmetric optimization," European Journal of Operational Research, Elsevier, vol. 214(3), pages 473-484, November.
    • Handle: RePEc:eee:ejores:v:214:y:2011:i:3:p:473-484
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    1. 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.
    2. NESTEROV , Yurii & TODD , Michael, 1995. "Primal-Dual Interior-Point Methods for Self-Scaled Cones," LIDAM Discussion Papers CORE 1995044, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. 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.
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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.
    2. Behrouz Kheirfam, 2013. "A new infeasible interior-point method based on Darvay’s technique for symmetric optimization," Annals of Operations Research, Springer, vol. 211(1), pages 209-224, December.
    3. Soodabeh Asadi & Hossein Mansouri & Zsolt Darvay & Maryam Zangiabadi & Nezam Mahdavi-Amiri, 2019. "Large-Neighborhood Infeasible Predictor–Corrector Algorithm for Horizontal Linear Complementarity Problems over Cartesian Product of Symmetric Cones," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 811-829, March.
    4. Chee-Khian Sim, 2019. "Interior point method on semi-definite linear complementarity problems using the Nesterov–Todd (NT) search direction: polynomial complexity and local convergence," Computational Optimization and Applications, Springer, vol. 74(2), pages 583-621, November.
    5. Alireza Asadi & Cornelis Roos, 2016. "Infeasible Interior-Point Methods for Linear Optimization Based on Large Neighborhood," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 562-590, August.
    6. G. Q. Wang & Y. Q. Bai, 2012. "A Class of Polynomial Interior Point Algorithms for the Cartesian P-Matrix Linear Complementarity Problem over Symmetric Cones," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 739-772, March.
    7. Ximei Yang & Hongwei Liu & Yinkui Zhang, 2015. "A New Strategy in the Complexity Analysis of an Infeasible-Interior-Point Method for Symmetric Cone Programming," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 572-587, August.
    8. Changhe Liu & Hongwei Liu & Xinze Liu, 2012. "Polynomial Convergence of Second-Order Mehrotra-Type Predictor-Corrector Algorithms over Symmetric Cones," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 949-965, September.
    9. Xiaoni Chi & Guoqiang Wang, 2021. "A Full-Newton Step Infeasible Interior-Point Method for the Special Weighted Linear Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 108-129, July.
    10. G. Q. Wang & Y. Q. Bai & X. Y. Gao & D. Z. Wang, 2015. "Improved Complexity Analysis of Full Nesterov–Todd Step Interior-Point Methods for Semidefinite Optimization," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 242-262, April.
    11. Ali Mohammad-Nezhad & Tamás Terlaky, 2017. "A polynomial primal-dual affine scaling algorithm for symmetric conic optimization," Computational Optimization and Applications, Springer, vol. 66(3), pages 577-600, April.
    12. 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.
    13. Petra Renáta Rigó & Zsolt Darvay, 2018. "Infeasible interior-point method for symmetric optimization using a positive-asymptotic barrier," Computational Optimization and Applications, Springer, vol. 71(2), pages 483-508, November.
    14. G. Q. Wang & L. C. Kong & J. Y. Tao & G. Lesaja, 2015. "Improved Complexity Analysis of Full Nesterov–Todd Step Feasible Interior-Point Method for Symmetric Optimization," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 588-604, August.
    15. Hongwei Liu & Ximei Yang & Changhe Liu, 2013. "A New Wide Neighborhood Primal–Dual Infeasible-Interior-Point Method for Symmetric Cone Programming," Journal of Optimization Theory and Applications, Springer, vol. 158(3), pages 796-815, September.

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