Afrika Matematika

, Volume 28, Issue 3–4, pp 389–406 | Cite as

A primal-dual interior-point algorithm for symmetric optimization based on a new kernel function with trigonometric barrier term yielding the best known iteration bounds

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Abstract

Kernel functions play an important role in defining new search directions for primal-dual interior-point algorithms for solving symmetric optimization problems. In this paper we present a new kernel function for which interior point method yields iteration bounds \({\mathcal {O}}(\sqrt{r}\log r\log \frac{r}{\epsilon })\) and \({\mathcal {O}}(\sqrt{r}\log \frac{r}{\epsilon })\) for large-and small-update methods, respectively, which matches currently the best known bounds for such methods.

Keywords

Primal-dual interior-point methods Symmetric optimization Polynomial complexity Kernel function 

Mathematics Subject Classification

90C51 

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Copyright information

© African Mathematical Union and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Applied MathematicsAzarbaijan Shahid Madani UniversityTabrizIslamic Republic of Iran

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