# An interior-point algorithm for $P_{\ast}(\kappa)$-linear complementarity problem based on a new trigonometric kernel function

Document Type: Research Paper

Authors

1 Department of Mathematics, Shiraz University of Technology, Shiraz, Iran

2 Department of Applied Mathematics, Shahrekord University, Shahrekord, Iran

3 Faculty of Mathematics, K.N. Toosi Univ. of Tech., Tehran, Iran

Abstract

In this paper, an interior-point algorithm  for $P_{\ast}(\kappa)$-Linear Complementarity Problem (LCP) based on a new parametric trigonometric kernel function is proposed. By applying strictly feasible starting point condition and using some simple analysis tools, we prove that our algorithm has $O((1+2\kappa)\sqrt{n} \log n\log\frac{n}{\epsilon})$ iteration bound for large-update methods, which coincides with the best known complexity bound. Moreover, numerical results confirm that our new proposed kernel function is doing well in practice in comparison with some existing kernel functions in the literature.

Keywords