Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2016; 53(6): 1831-1844

Online first article September 29, 2016      Printed November 30, 2016

https://doi.org/10.4134/BKMS.b151016

Copyright © The Korean Mathematical Society.

An adaptive primal-dual full-Newton step infeasible interior-point algorithm for linear optimization

Soodabeh Asadi, Hossein Mansouri, and Maryam Zangiabadi

Shahrekord University, Shahrekord University, Shahrekord University

Abstract

In this paper, we improve the full-Newton step infeasible interior-point algorithm proposed by Mansouri et al. \cite{Arzani}. The algorithm takes only one full-Newton step in a major iteration. To perform this step, the algorithm adopts the largest logical value for the barrier update parameter $\theta$. This value is adapted with the value of proximity function $\delta$ related to $(x\k y\k s)$ in current iteration of the algorithm. We derive a suitable interval to change the parameter $\theta$ from iteration to iteration. This leads to more flexibilities in the algorithm, compared to the situation that $\theta$ takes a default fixed value.

Keywords: linear optimization, infeasible interior-point method, central path, adaptive updating

MSC numbers: 90C51, 90C05, 49M15

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