# A NEW PRIMAL-DUAL INTERIOR POINT METHOD FOR LINEAR OPTIMIZATION

• Cho, Gyeong-Mi (DEPARTMENT OF MULTIMEDIA ENGINEERING, DONGSEO UNIVERSITY)
• Accepted : 2009.03.06
• Published : 2009.03.25

#### Abstract

A primal-dual interior point method(IPM) not only is the most efficient method for a computational point of view but also has polynomial complexity. Most of polynomialtime interior point methods(IPMs) are based on the logarithmic barrier functions. Peng et al.([14, 15]) and Roos et al.([3]-[9]) proposed new variants of IPMs based on kernel functions which are called self-regular and eligible functions, respectively. In this paper we define a new kernel function and propose a new IPM based on this kernel function which has $O(n^{\frac{2}{3}}log\frac{n}{\epsilon})$ and $O(\sqrt{n}log\frac{n}{\epsilon})$ iteration bounds for large-update and small-update methods, respectively.

#### Acknowledgement

Supported by : Korea Research Foundation

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