Periodica Mathematica Hungarica

, Volume 73, Issue 1, pp 27–42

# Complexity analysis of a full-Newton step interior-point method for linear optimization

Article

## Abstract

This paper concerns a short-update primal-dual interior-point method for linear optimization based on a new search direction. We apply a vector-valued function generated by a univariate function on the nonlinear equation of the system which defines the central path. The common way to obtain the equivalent form of the central path is using the square root function. In this paper we consider a new function formed by the difference of the identity map and the square root function. We apply Newton’s method in order to get the new directions. In spite of the fact that the analysis is more difficult in this case, we prove that the complexity of the algorithm is identical with the one of the best known methods for linear optimization.

## Keywords

Linear optimization Interior-point method Full-Newton step Search direction Polynomial complexity

90C05 90C51

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## Authors and Affiliations

• Zsolt Darvay
• 1
Email author
• Ingrid-Magdolna Papp
• 1
• Petra-Renáta Takács
• 1
1. 1.Faculty of Mathematics and Computer ScienceBabeş-Bolyai UniversityCluj-NapocaRomania

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