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Counter Example to A Conjecture on Infeasible Interior-Point Methods

G. Gu(g.gu***at***tudelft.nl)
C. Roos(c.roos***at***tudelft.nl)

Abstract: Based on extensive computational evidence (hundreds of thousands of randomly generated problems) the second author conjectured that $\bar{\kappa}(\zeta)=1$, which is a factor of $\sqrt{2n}$ better than that has been proved, and which would yield an $O(\sqrt{n})$ iteration full-Newton step infeasible interior-point algorithm. In this paper we present an example showing that $\bar{\kappa}(\zeta)$ is in the order of $\sqrt{n}$, the same order as that has been proved. In other words, the current best iteration bound for infeasible interior-point algorithms cannot be improved.

Keywords: linear optimization, infeasible interior-point method, full-Newton step method, conjecture

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

Citation: July/2008

Download: [PDF]

Entry Submitted: 12/05/2008
Entry Accepted: 12/05/2008
Entry Last Modified: 12/05/2008

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