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On self-regular IPMs

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Abstract

Primal-dual interior-point methods (IPMs) have shown their power in solving large classes of optimization problems. However, at present there is still a gap between the practical behavior of these algorithms and their theoretical worst-case complexity results, with respect to the strategies of updating the duality gap parameter in the algorithm. The so-called small-update IPMs enjoy the best known theoretical worst-case iteration bound, but work very poorly in practice. To the contrary, the so-called large-update IPMs have superior practical performance but with relatively weaker theoretical results. In this paper we discuss the new algorithmic variants and improved complexity results with respect to the new family of Self-Regular proximity based IPMs for Linear Optimization problems, and their generalizations to Conic and Semidefinite Optimization

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Authors and Affiliations

  1. Department of Mathematics and Statistics, McMaster University, L8S 4K1, Hamilton, ON, Canada

    Maziar Salahi

  2. Advanced Optimization Laboratory, Department of Computing & Software, McMaster University, L8S 4K1, Hamilton, ON, Canada

    Renata Sotirov & Tamás Terlaky

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  1. Maziar Salahi
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  2. Renata Sotirov
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  3. Tamás Terlaky
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Additional information

This research was supported by the MITACS project “New IPMs and Software for Convex Conic-Linear Optimization and Their Application to Solve VLSI Circuit Layout Problems”, by an NSERC discovery grant, and the CRC program. The first author would also like to thank the Iranian Ministry of Science, Research and Technology for supporting his research.

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Salahi, M., Sotirov, R. & Terlaky, T. On self-regular IPMs. Top 12, 209–275 (2004). https://doi.org/10.1007/BF02578956

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