An interior-point algorithm for \(P_*(\kappa )\) -LCP based on a new trigonometric kernel function with a double barrier term
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- 作者：Xin Li ; Mingwang Zhang ; Yan Chen
- 关键词：Linear complementarity problem ; Kernel function ; Interior ; point algorithm ; Large ; update ; Iteration complexity
- 刊名：Journal of Applied Mathematics and Computing
- 出版年：2017
- 出版时间：February 2017
- 年：2017
- 卷：53
- 期：1-2
- 页码：487-506
- 全文大小：
- 刊物类别：Mathematics and Statistics
- 刊物主题：Computational Mathematics and Numerical Analysis; Appl.Mathematics/Computational Methods of Engineering; Theory of Computation; Mathematics of Computing;
- 出版者：Springer Berlin Heidelberg
- ISSN：1865-2085
- 卷排序：53
文摘
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.