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

• Published in: Journal of applied mathematics & computing Vol. 53; no. 1-2; pp. 487 - 506
• Main Authors: Li, Xin, Zhang, Mingwang, Chen, Yan
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2017
• Subjects: Computational Mathematics and Numerical Analysis; Mathematical and Computational Engineering; Mathematics; Mathematics and Statistics; Mathematics of Computing; Original Research; Theory of Computation; Iteration complexity; Kernel function; 90C51; 90C33; Interior-point algorithm; Large-update; Linear complementarity problem
• ISSN: 1598-5865; 1865-2085
• DOI: 10.1007/s12190-015-0978-3

In this paper, we present a new large-update interior-point algorithm for P ∗ ( κ ) -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 κ ) n 2 3 log n ε ) 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 ∗ ( κ ) -linear complementarity problem based on trigonometric kernel functions.