A new large-update interior point algorithm for P ( κ ) linear complementarity problems

• Published in: Journal of computational and applied mathematics Vol. 216; no. 1; pp. 265 - 278
• Main Author: Cho, Gyeong-Mi
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15.06.2008; Elsevier
• Subjects: 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; Polynomial algorithm; Sciences and techniques of general use; Kernel function; 65K05; 90C33; 49M15; Linear complementarity problem; Polynomial algorithm; Large-update interior point method; Complexity; Polynomial; Logarithmic function; Optimization method; Interior point method; Complementarity problem; Algorithm; 90C33,Large-update interior point method; Numerical analysis; Applied mathematics; Software; Mathematical programming
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2007.05.007

In this paper we propose a new large-update primal-dual interior point algorithm for P * ( κ ) linear complementarity problems (LCPs). We generalize Bai et al.'s [A primal-dual interior-point method for linear optimization based on a new proximity function, Optim. Methods Software 17(2002) 985–1008] primal-dual interior point algorithm for linear optimization (LO) problem to P * ( κ ) LCPs. New search directions and proximity measures are proposed based on a kernel function which is not logarithmic barrier nor self-regular for P * ( κ ) LCPs. We showed that if a strictly feasible starting point is available, then the new large-update primal-dual interior point algorithm for solving P * ( κ ) LCPs has the polynomial complexity O ( ( 1 + 2 κ ) n 3 / 4 log ( n / ε ) ) and gives a simple complexity analysis. This proximity function has not been used in the complexity analysis of interior point method (IPM) for P * ( κ ) LCPs before.