Interior point algorithm for P* nonlinear complementarity problems

Authors:
Min-Kyung Kim;Gyeong-Mi Cho
Affiliations:
Department of Mathematics, Pusan National University, Busan 609-735, South Korea;Department of Multimedia Engineering, Dongseo University, Busan 617-716, South Korea
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

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Abstract

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 @j(t)=(t^p^+^1-1)/(p+1)+(t^-^q-1)/q,p@?[0,1], q0. 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@k)nlognlog(n@m^0/@e)) iteration complexity which is currently the best known result for such methods with p=1 and q=(logn)/2-1.