A Class of New Large-Update Primal-Dual Interior-Point Algorithms for P*(κ) Linear Complementarity Problems

A class of polynomial primal-dual interior-point algorithms for P-*(kappa) linear complementarity problems (LCPs) are presented. We generalize Ghami et al.'s[A polynomial-time algorithm for linear optimization based on a new class of kernel functions(2008)] algorithm for linear optimation (LO) problem P-*(kappa) LCPs. Our analysis is based on a class of finite kernel functions which have the linear and quadratic growth terms. Since P-*(kappa) LCP is a generalization of LO problem, we lose the orthogonality of the vectors dx and ds. So our analysis is different from the one in Ghami et al's algorithm. Despite this, the favorable complexity result is obtained, namely, O((1+2 kappa)n(1/1+P) log n log(n/epsilon)), which is better than the usual large-update primal-dual algorithm based on the classical logarithmic barrier function for P-*(kappa) LCPs.