Large-update interior point algorithm for P∗-linear complementarity problem

• Published in: Journal of inequalities and applications Vol. 2014; no. 1
• Main Author: Cho, Gyeong-Mi
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 24.09.2014
• Subjects: Analysis; Applications of Mathematics; Mathematics; Mathematics and Statistics; Thematic Series in the Honor of Professor Shih-Sen Chang’s(张石生) 80th birthday and his significant contributions to Nonlinear Analysis and its Applications; complexity; interior point method; linear complementarity problem; barrier function
• ISSN: 1029-242X; 1025-5834; 1029-242X
• DOI: 10.1186/1029-242X-2014-363

It is well known that each barrier function defines an interior point algorithm and each barrier function is determined by its univariate kernel function. In this paper we present a new large-update primal-dual interior point algorithm for solving P ∗ -linear complementarity problem (LCP) based on a parametric version of the kernel function in (Bai et al. in SIAM J. Optim. 13:766-782, 2003). We show that the algorithm has O ( ( 1 + 2 κ ) ( log p ) 3 n ( log n ) log n μ 0 ϵ ) iteration complexity, where p is a barrier function parameter and κ is the handicap of the matrix. This is the best known complexity result for such a method. MSC: 90C33, 90C51.