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A tight iteration-complexity upper bound for the MTY predictor-corrector algorithm via redundant Klee-Minty cubes

Murat Mut(mhm309***at***lehigh.edu)
Tamás Terlaky(terlaky***at***lehigh.edu)

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 $\epsilon >0$, there is a redundant Klee-Minty cube for which the aforementioned algorithm requires $n^{( \frac{1}{2}-\epsilon )} $ 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.

Keywords: Curvature, Central path, Polytopes , Complexity, Interior-point methods, Linear optimization

Category 1: Linear, Cone and Semidefinite Programming (Linear Programming )

Citation:

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Entry Submitted: 08/14/2014
Entry Accepted: 08/14/2014
Entry Last Modified: 08/14/2014

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