On the Rate of Local Convergence of High-Order-Infeasible-Path-Following Algorithms for P*-Linear Complementarity Problems

A simple and uniied analysis is provided on the rate of local convergence for a class of high-order-infeasible-path-following algorithms for the P-linear complementarity problem (P-LCP). It is shown that the rate of local convergence of a-order algorithm with a centering step is + 1 if there is a strictly complementary solution and (+ 1)=2 otherwise. For the-order algorithm without the centering step the corresponding rates are and =2, respectively. The algorithm without a centering step does not follow the xed traditional central path. Instead, at each iteration, it follows a new analytic path connecting the current iterate with an optimal solution to generate the next iterate. An advantage of this algorithm is that it does not restrict iterates in a sequence of contracting neighborhoods of the central path. Abbreviated Title. Local convergence of high-order algorithms for P-LCP AMS(MOS) subject classiications. 90C33