A NEW LARGE-UPDATE INTERIOR POINT ALGORITHM FOR P¤(·) LCPS BASED ON A KERNEL FUNCTION

In this paper we present a new large-update primal-dual interior point algorithm for P¤(·)-linear complementarity problems (P¤(·)- LCPs). We introduce a new class of kernel functions which are not logarithmic barrier nor self-regular in the complexity analysis of interior point method (IPM) for P¤(·)-LCP. If a strictly feasible starting point is available, the new large-update primal-dual interior point algorithms for this problem have the polynomial complexity O(q(1 + 2·) p n(log n) q+1 q log n " ) which is better than the classical large-update primal-dual algorithm based on the logarithmic barrier function