Abstract
Long step interior-point methods in linear programming are some of the most efficientalgorithms from a computational point of view. We prove polynomial complexity of a classof long step target-following methods in a novel way, by introducing a new nonconvexpotential function and adapting the analysis framework of Jansen et al. [4, 6, 7]. The mainadvantage is that the new potential function has an obvious extension to semi-definiteprogramming, whereas the potential used in the above-mentioned papers does not.
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de Klerk, E., Roos, C. & Terlaky, T. A nonconvex weighted potential function forpolynomial target following methods. Annals of Operations Research 81, 3–14 (1998). https://doi.org/10.1023/A:1018913325452
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DOI: https://doi.org/10.1023/A:1018913325452