Counter Example to a Conjecture on Infeasible Interior-point Methods
نویسنده
چکیده
Based on extensive computational evidence (hundreds of thousands of randomly generated problems) the second author conjectured that κ̄(ζ) = 1 (Conjecture 5.1 in [1]), which is a factor of √ 2n better than has been proved in [1], and which would yield an O( √ n) iteration full-Newton step infeasible interior-point algorithm. In this paper we present an example showing that κ̄(ζ) is in the order of √ n, the same order as has been proved in [1]. In other words, the current best iteration bound for infeasible interior-point algorithms cannot be improved.
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