AN ELIGIBLE KERNEL BASED PRIMAL-DUAL INTERIOR-POINT METHOD FOR LINEAR OPTIMIZATION

• Journal title : Honam Mathematical Journal
• Volume 35, Issue 2,  2013, pp.235-249
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2013.35.2.235
Title & Authors
AN ELIGIBLE KERNEL BASED PRIMAL-DUAL INTERIOR-POINT METHOD FOR LINEAR OPTIMIZATION
Cho, Gyeong-Mi;

Abstract
It is well known that each kernel function defines primal-dual interior-point method (IPM). Most of polynomial-time interior-point algorithms for linear optimization (LO) are based on the logarithmic kernel function ([9]). In this paper we define new eligible kernel function and propose a new search direction and proximity function based on this function for LO problems. We show that the new algorithm has $\small{\mathcal{O}(({\log}\;p)^{\frac{5}{2}}\sqrt{n}{\log}\;n\;{\log}\frac{n}{\epsilon})}$ and $\small{\mathcal{O}(q^{\frac{3}{2}}({\log}\;p)^3\sqrt{n}{\log}\;\frac{n}{\epsilon})}$ iteration complexity for large- and small-update methods, respectively. These are currently the best known complexity results for such methods.
Keywords
primal-dual interior point method;kernel function;complexity;polynomial algorithm;linear optimization;
Language
English
Cited by
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