Abstract
By refining a variant of the Klee–Minty example that forces the central path to visit all the vertices of the Klee–Minty n-cube, we exhibit a nearly worst-case example for path-following interior point methods. Namely, while the theoretical iteration-complexity upper bound is \(O(2^{n}n^{\frac{5}{2}})\), we prove that solving this n-dimensional linear optimization problem requires at least 2n−1 iterations.
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Dedicated to Professor Emil Klafszky on the occasion of his 70th birthday.
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Deza, A., Nematollahi, E. & Terlaky, T. How good are interior point methods? Klee–Minty cubes tighten iteration-complexity bounds. Math. Program. 113, 1–14 (2008). https://doi.org/10.1007/s10107-006-0044-x
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DOI: https://doi.org/10.1007/s10107-006-0044-x