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Further development of multiple centrality correctors for interior point methods

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Abstract

This paper addresses the role of centrality in the implementation of interior point methods. We provide theoretical arguments to justify the use of a symmetric neighbourhood, and translate them into computational practice leading to a new insight into the role of re-centering in the implementation of interior point methods. Second-order correctors, such as Mehrotra’s predictor–corrector, can occasionally fail: we derive a remedy to such difficulties from a new interpretation of multiple centrality correctors. Through extensive numerical experience we show that the proposed centrality correcting scheme leads to noteworthy savings over second-order predictor–corrector technique and previous implementations of multiple centrality correctors.

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Authors and Affiliations

  1. School of Mathematics, The University of Edinburgh, Mayfield Road, Edinburgh, EH9 3JZ, UK

    Marco Colombo & Jacek Gondzio

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  1. Marco Colombo
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  2. Jacek Gondzio
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Correspondence to Marco Colombo.

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Colombo, M., Gondzio, J. Further development of multiple centrality correctors for interior point methods. Comput Optim Appl 41, 277–305 (2008). https://doi.org/10.1007/s10589-007-9106-0

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  • DOI: https://doi.org/10.1007/s10589-007-9106-0

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