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New Predictor–Corrector Algorithm for Symmetric Cone Horizontal Linear Complementarity Problems

Author

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  • Zsolt Darvay

    (Babeş-Bolyai University, Corvinus University of Budapest
    Corvinus University of Budapest)

  • Petra Renáta Rigó

    (Corvinus University of Budapest)

Abstract

We propose a new predictor–corrector interior-point algorithm for solving Cartesian symmetric cone horizontal linear complementarity problems, which is not based on a usual barrier function. We generalize the predictor–corrector algorithm introduced in Darvay et al. (SIAM J Optim 30:2628–2658, 2020) to horizontal linear complementarity problems on a Cartesian product of symmetric cones. We apply the algebraically equivalent transformation technique proposed by Darvay (Adv Model Optim 5:51–92, 2003), and we use the difference of the identity and the square root function to determine the new search directions. In each iteration, the proposed algorithm performs one predictor and one corrector step. We prove that the predictor–corrector interior-point algorithm has the same complexity bound as the best known interior-point methods for solving these types of problems. Furthermore, we provide a condition related to the proximity and update parameters for which the introduced predictor-corrector algorithm is well defined.

Suggested Citation

  • Zsolt Darvay & Petra Renáta Rigó, 2024. "New Predictor–Corrector Algorithm for Symmetric Cone Horizontal Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 202(1), pages 50-75, July.
    • Handle: RePEc:spr:joptap:v:202:y:2024:i:1:d:10.1007_s10957-022-02078-z
    DOI: 10.1007/s10957-022-02078-z
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    References listed on IDEAS

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    1. Tibor Illés & Marianna Nagy & Tamás Terlaky, 2010. "A polynomial path-following interior point algorithm for general linear complementarity problems," Journal of Global Optimization, Springer, vol. 47(3), pages 329-342, July.
    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.
    3. 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.
    4. de Klerk, E. & Roos, C. & Terlaky, T., 1997. "Initialization in semidefinite programming via a self-dual, skew-symmetric embedding," Other publications TiSEM aa045849-1e10-4f84-96ca-4, Tilburg University, School of Economics and Management.
    5. Illes, Tibor & Nagy, Marianna, 2007. "A Mizuno-Todd-Ye type predictor-corrector algorithm for sufficient linear complementarity problems," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1097-1111, September.
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