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Erschienen in:
2019 | OriginalPaper | Buchkapitel
The Iteration-Complexity Upper Bound for the Mizuno-Todd-Ye Predictor-Corrector Algorithm is Tight
verfasst von : Murat Mut, Tamás Terlaky
Erschienen in: Modeling and Optimization: Theory and Applications
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Abstract
It is an open question whether there is an interior-point algorithm for linear optimization problems with a lower iteration-complexity than the classical bound \(\mathcal {O}(\sqrt{n} \log (\frac{\mu _1}{\mu _0}))\). This paper provides a negative answer to that question for a variant of the Mizuno-Todd-Ye predictor-corrector algorithm. In fact, we prove that for any \(\varepsilon >0\), there is a redundant Klee-Minty cube for which the aforementioned algorithm requires \(n^{( \frac{1}{2}-\varepsilon )} \) iterations to reduce the barrier parameter by at least a constant. This is provably the first case of an adaptive step interior-point algorithm where the classical iteration-complexity upper bound is shown to be tight.