- A tight iteration-complexity upper bound for the MTY predictor-corrector algorithm via redundant Klee-Minty cubes Murat Mut(mhm309lehigh.edu) Tamás Terlaky(terlakylehigh.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: Download: [PDF]Entry Submitted: 08/14/2014Entry Accepted: 08/14/2014Entry Last Modified: 08/14/2014Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.