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Corrector-Predictor Interior-Point Method With New Search Direction for Semidefinite Optimization

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Abstract

In this paper, we present a new corrector-predictor interior-point method for solving semidefinite optimization. We use an algebraic equivalent transformation of the centering equation of the system which defines the central path. The algebraic transformation plays an essential role in the calculation of the new search directions. We prove that the iteration complexity of the algorithm coincides with the best known ones for interior-point methods (IPMs). To the best of our knowledge, this is the first corrector-predictor interior-point algorithm that uses the search directions obtained from the desired algebraic transformation for semidefinite optimization. Finally, some numerical experiments are provided to demonstrate the efficiency of our new algorithm.

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Acknowledgements

The author would like to thank the editor and the anonymous referees for their careful reading of the paper, and for their constructive remarks that greatly helped to improve its presentation. The author is also grateful to N. Osmanpour for his assistance in the numerical results.

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  1. Department of Applied Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

    B. Kheirfam

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Kheirfam, B. Corrector-Predictor Interior-Point Method With New Search Direction for Semidefinite Optimization. J Sci Comput 95, 10 (2023). https://doi.org/10.1007/s10915-023-02137-1

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