Interior point algorithm for P ∗ nonlinear complementarity problems

• Published in: Journal of computational and applied mathematics Vol. 235; no. 13; pp. 3751 - 3759
• Main Authors: Kim, Min-Kyung, Cho, Gyeong-Mi
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Kidlington Elsevier B.V 01.05.2011; Elsevier
• Subjects: Complementarity problem; Complexity; Exact sciences and technology; Kernel function; Large-update primal–dual interior point method; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Polynomial algorithm; Sciences and techniques of general use; Large-update primal–dual interior point method; Kernel function; Complementarity problem; Polynomial algorithm; Complexity; Polynomial; Logarithmic function; Interior point method; Iteration; Nonlinear problems; Large-update primal-dual interior point method; Algorithm; Numerical analysis; Applied mathematics
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2011.01.021

In this paper, we propose a new large-update primal–dual interior point algorithm for P ∗ complementarity problems (CPs). Different from most interior point methods which are based on the logarithmic kernel function, the new method is based on a class of kernel functions ψ ( t ) = ( t p + 1 − 1 ) / ( p + 1 ) + ( t − q − 1 ) / q , p ∈ [ 0 , 1 ] , q > 0 . We show that if a strictly feasible starting point is available and the undertaken problem satisfies some conditions, then the new large-update primal–dual interior point algorithm for P ∗ CPs has O ( ( 1 + 2 κ ) n log n log ( n μ 0 / ε ) ) iteration complexity which is currently the best known result for such methods with p = 1 and q = ( log n ) / 2 − 1 .