An interior-point algorithm for $$P_*(\kappa )$$ P ∗ ( κ ) -LCP based on a new trigonometric kernel function with a double barrier term

Abstract

In this paper, we present a new large-update interior-point algorithm for \(P_*(\kappa )\)-linear complementarity problem. The new algorithm is based on a trigonometric kernel function which differs from the existing kernel functions in which it has a double barrier term. By a simple analysis, we show that the new algorithm enjoys \({ O}((1+2\kappa )n^\frac{2}{3}\log \frac{n}{\varepsilon })\) iteration complexity. This complexity estimate improves a result from El Ghami et al. (Optim Theory Decis Mak Oper Res Appl 31: 331–349, 2013) and matches the currently best known complexity result for \(P_*(\kappa )\)-linear complementarity problem based on trigonometric kernel functions.