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A PRIMAL-DUAL INTERIOR-POINT ALGORITHM BASED ON A NEW KERNEL FUNCTION

Published online by Cambridge University Press:  03 February 2011

G. M. CHO ,
Y. Y. CHO  and
Y. H. LEE
G. M. CHO*
Affiliation:
Department of Multimedia Engineering, Dongseo University, Busan 617-716, South Korea (email: gcho@dongseo.ac.kr)
Y. Y. CHO
Affiliation:
Department of Mathematics, Pusan National University, Busan 609-735, South Korea (email: youyoung@pusan.ac.kr)
Y. H. LEE
Affiliation:
Department of Mathematics, Pusan National University, Busan 609-735, South Korea (email: yhlee@pusan.ac.kr)
*
✉For correspondence; e-mail: gcho@dongseo.ac.kr
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Abstract

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We propose a new primal-dual interior-point algorithm based on a new kernel function for linear optimization problems. New search directions and proximity functions are proposed based on the kernel function. We show that the new algorithm has $\mathcal {O}(\sqrt {n} \log n \log ({n}/{\epsilon }))$ and $\mathcal {O}(\sqrt {n}\log ({n}/{\epsilon }))$ iteration bounds for large-update and small-update methods, respectively, which are currently the best known bounds for such methods.

Keywords

primal-dual interior-point methodkernel functioncomplexitypolynomial algorithmlinear optimization problem

MSC classification

Secondary: 90C05: Linear programming

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 51 , Issue 4 , April 2010 , pp. 476 - 491
Copyright
Copyright © Australian Mathematical Society 2011

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