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A logarithmic barrier interior-point method based on majorant functions for second-order cone programming

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Abstract

We present a logarithmic barrier interior-point method for solving a second-order cone programming problem. Newton’s method is used to compute the descent direction. The main contribution of this paper is that it uniquely uses the so-called majorant functions as an efficient alternative to line search methods to determine the displacement step along the direction while solving second-order cone programs. The efficiency of our method is shown by presenting numerical experiments.

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Acknowledgements

The work of the author was supported in part by the Deanship of Scientific Research at The University of Jordan. The author thanks the anonymous referees for their valuable suggestions, their constructive comments have greatly enhanced the paper.

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  1. Department of Mathematics, The University of Jordan, Amman, 11942, Jordan

    Baha Alzalg

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  1. Baha Alzalg
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Correspondence to Baha Alzalg.

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Alzalg, B. A logarithmic barrier interior-point method based on majorant functions for second-order cone programming. Optim Lett 14, 729–746 (2020). https://doi.org/10.1007/s11590-019-01404-1

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