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Novel Kernel Function With a Hyperbolic Barrier Term to Primal-dual Interior Point Algorithm for SDP Problems

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Abstract

In this paper, we introduce for the first time a new eligible kernel function with a hyperbolic barrier term for semidefinite programming (SDP). This add a new type of functions to the class of eligible kernel functions. We prove that the interior-point algorithm based on the new kernel function meets \({\cal O}({n^{{3 \over 4}}}\log {n \over \varepsilon })\) iterations as the worst case complexity bound for the large-update method. This coincides with the complexity bound obtained by the first kernel function with a trigonometric barrier term proposed by El Ghami et al. in 2012, and improves with a factor \({n^{{1 \over 4}}}\) the obtained iteration bound based on the classic kernel function. We present some numerical simulations which show the effectiveness of the algorithm developed in this paper.

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Acknowledgments

The authors are very grateful and would like to thank the Editor-in-Chief and the anonymous referees for their suggestions and helpful comments which significantly improved the presentation of this paper.

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  1. LMPA, Mohammed Seddik Ben Yahia University, Jijel, 18000, Algeria

    Imene Touil & Wided Chikouche

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  1. Imene Touil
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  2. Wided Chikouche
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Correspondence to Imene Touil.

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Touil, I., Chikouche, W. Novel Kernel Function With a Hyperbolic Barrier Term to Primal-dual Interior Point Algorithm for SDP Problems. Acta Math. Appl. Sin. Engl. Ser. 38, 44–67 (2022). https://doi.org/10.1007/s10255-022-1061-0

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