An interior-point method for $$P_*(\kappa )$$ P ∗ ( κ ) -linear complementarity problem based on a trigonometric kernel function

Abstract

Recently, El Ghami (Optim Theory Decis Mak Oper Res Appl 31:331–349, 2013) proposed a primal dual interior point method for $$P_*(\kappa )$$ -Linear Complementarity Problem (LCP) based on a trigonometric barrier term and obtained the worst case iteration complexity as $$O\left( (1+2\kappa )n^{\frac{3}{4}}\log \frac{n}{\epsilon }\right) $$ for large-update methods. In this paper, we present a large update primal–dual interior point algorithm for $$P_{*}(\kappa )$$ -LCP based on a new trigonometric kernel function. By a simple analysis, we show that our algorithm based on the new kernel function enjoys the worst case $$O\left( (1+2\kappa )\sqrt{n}\log n\log \frac{n}{\epsilon }\right) $$ iteration bound for solving $$P_*(\kappa )$$ -LCP. This result improves the worst case iteration bound obtained by El Ghami for $$P_*(\kappa )$$ -LCP based on trigonometric kernel functions significantly.