A new full-Newton step interior-point method for P∗(κ)-LCP based on a positive-asymptotic kernel function

• Published in: Journal of applied mathematics & computing Vol. 64; no. 1-2; pp. 313 - 330
• Main Authors: Zhang, Mingwang, Huang, Kun, Li, Mengmeng, Lv, Yanli
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2020; Springer Nature B.V
• Subjects: Algorithms; Applied mathematics; Asymptotic methods; Asymptotic properties; Complexity; Computational Mathematics and Numerical Analysis; Iterative methods; Kernel functions; Mathematical and Computational Engineering; Mathematics; Mathematics and Statistics; Mathematics of Computing; Numerical methods; Optimization; Original Research; Theory of Computation; 90C51; 90C30; Full-Newton step; Positive-asymptotic kernel function; LCPs; 90C05; IPMs
• ISSN: 1598-5865; 1865-2085
• DOI: 10.1007/s12190-020-01356-1

In this paper, we propose a new full-Newton step interior-point method (IPM) for P ∗ ( κ ) linear complementarity problem (LCP). The search direction is obtained by applying algebraic equivalent transformation on the centering equation of the central path which is introduced by Darvay et al. for linear optimization (Optim Lett 12(5):1099–1116, 2018). They point out that the search direction can also be obtained by using a positive-asymptotic kernel function. This kernel function has not been used in the complexity analysis of IPMs for P ∗ ( κ ) -LCP before. Assuming a strictly feasible starting point is available, we show that the algorithm has the iteration complexity bound O ( ( 1 + 4 κ ) n log n ϵ ) , which is the best known complexity result for such methods. Some numerical results have been provided.