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A primal-dual interior-point method based on various selections of displacement step for symmetric optimization

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Abstract

In this paper, we develop a primal-dual central trajectory interior-point algorithm for symmetric programming problems and establish its complexity analysis. The main contribution of the paper is that it uniquely equips the central trajectory algorithm with various selections of the displacement step while solving symmetric programming. To show the efficiency of the proposed algorithm, these selections of calculating the displacement step are compared in numerical examples for second-order cone programming, which is a special case of symmetric programming.

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Notes

  1. The direct sum of two square matrices A and B is the block diagonal matrix \(A \oplus B := \left[ \begin{array}{cc} A&{}0\\ 0&{}B\\ \end{array} \right] \).

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Acknowledgements

A part of this work was performed while the author was visiting The Center for Applied and Computational Mathematics at Rochester Institute of Technology, NY, USA. The work of the author was supported in part by the Deanship of Scientific Research at the University of Jordan. The author thanks the two anonymous expert referees for their valuable suggestions. The constructive comments from the referees have greatly enhanced the paper.

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Authors and Affiliations

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

    Baha Alzalg

  2. School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY, 14623, USA

    Baha Alzalg

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  1. Baha Alzalg
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Correspondence to Baha Alzalg.

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Alzalg, B. A primal-dual interior-point method based on various selections of displacement step for symmetric optimization. Comput Optim Appl 72, 363–390 (2019). https://doi.org/10.1007/s10589-018-0045-8

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