Abstract
In this note we report a simple characteristic of linear programming central trajectories which has a surprising consequence. Specifically, we show that given a bounded polyhedral setP with nonempty interior, the logarithmic barrier function (with no objective component) induces a vector field of negative Newton directions which flows from the center ofP, along central trajectories, to solutions of every possible linear program onP.
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Anstreicher, K.M. Linear programming and the newton barrier flow. Mathematical Programming 41, 367–373 (1988). https://doi.org/10.1007/BF01580774
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DOI: https://doi.org/10.1007/BF01580774