# NEW INTERIOR POINT METHODS FOR SOLVING $P_*(\kappa)$ LINEAR COMPLEMENTARITY PROBLEMS

• Cho, You-Young (DEPARTMENT OF MATHEMATICS, PUSAN NATIONAL UNIVERSITY) ;
• Cho, Gyeong-Mi (DEPARTMENT OF MULTIMEDIA ENGINEERING, DONGSEO UNIVERSITY)
• Accepted : 2009.07.28
• Published : 2009.09.25

#### Abstract

In this paper we propose new primal-dual interior point algorithms for $P_*(\kappa)$ linear complementarity problems based on a new class of kernel functions which contains the kernel function in [8] as a special case. We show that the iteration bounds are $O((1+2\kappa)n^{\frac{9}{14}}\;log\;\frac{n{\mu}^0}{\epsilon}$) for large-update and $O((1+2\kappa)\sqrt{n}log\frac{n{\mu}^0}{\epsilon}$) for small-update methods, respectively. This iteration complexity for large-update methods improves the iteration complexity with a factor $n^{\frac{5}{14}}$ when compared with the method based on the classical logarithmic kernel function. For small-update, the iteration complexity is the best known bound for such methods.

#### Acknowledgement

Supported by : Korea Research Foundation