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Published in:
01-06-2015 | Original Research
An interior-point method for \(P_*(\kappa )\)-linear complementarity problem based on a trigonometric kernel function
Published in: Journal of Applied Mathematics and Computing | Issue 1-2/2015
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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.