New redundant constraints for Klee-Minty problem
by Bib Paruhum Silalahi
International Journal of Mathematical Modelling and Numerical Optimisation (IJMMNO), Vol. 11, No. 4, 2021

Abstract: Interior-point method (IPM) is a class of methods which has polynomial time for iteration complexity in solving linear optimisation problems. The iteration complexity upper bound of IPM can be stated as O(√N ln N), where N is the number of inequalities. In this paper, we prove that the new redundant constraints of the form: −ρy_k-1 − y_k ≤ d_k may cause the central path visits small neighbourhood of the vertices of the Klee-Minty cube. Our case has smaller number of redundant inequalities compared to best previous results, but of the same order: O(n2²ⁿ ). In our case the central path goes to at least 2ⁿ⁻¹ + 1 of the vertices (half of the vertices + 1).

Online publication date: Mon, 25-Oct-2021

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