A new large-update interior point algorithm for P ∗( κ) LCPs based on kernel functions

• Published in: Applied mathematics and computation Vol. 182; no. 2; pp. 1169 - 1183
• Main Authors: Cho, Gyeong-Mi, Kim, Min-Kyung
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 15.11.2006; Elsevier
• Subjects: Applied sciences; Calculus of variations and optimal control; Complexity; Exact sciences and technology; Kernel function; Large-update interior point method; Linear complementarity problem; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in mathematical programming, optimization and calculus of variations; Operational research and scientific management; Operational research. Management science; Optimization. Search problems; Polynomial algorithm; Sciences and techniques of general use; Kernel function; Linear complementarity problem; Polynomial algorithm; Large-update interior point method; Complexity; Logarithmic function; Barrier function; Optimization method; Interior point method; Complementarity problem; Gap problem; Numerical analysis; Applied mathematics; Primal dual method
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2006.04.060

In this paper we propose a new large-update primal-dual interior point algorithm for P ∗( κ) linear complementarity problems (LCPs). Recently, Peng et al. introduced self-regular barrier functions for primal-dual interior point methods (IPMs) for linear optimization (LO) problems and reduced the gap between the practical behavior of the algorithm and its theoretical worst case complexity. We introduce a new class of kernel functions which is not logarithmic barrier nor self-regular in the complexity analysis of interior point method (IPM) for P ∗( κ) linear complementarity problem (LCP). New search directions and proximity measures are proposed based on the kernel function. We showed that if a strictly feasible starting point is available, then the new large-update primal-dual interior point algorithms for solving P ∗( κ) LCPs have the polynomial complexity O q 3 2 ( 1 + 2 κ ) n ( log n ) q + 1 q log n ϵ which is better than the classical large-update primal-dual algorithm based on the classical logarithmic barrier function.