## On the rate of local convergence of high-order infeasible-path-following algorithms
for $P_*$-LCP with or without strictly complementary solutions

### Gongyun Zhao and Jie Sun

A very simple 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. It is shown that the rate of local convergence of a $\nu$-order algorithm with a
centering step is $\nu+1$ if there is a strictly complementary solution and $(\nu+1)/2$ if
there is not. For the $\nu$-order algorithm without the centering step the corresponding
rates are $\nu$ and $\nu/2$, respectively.

Research Report No. 698, Department of Mathematics, National University of Singapore,
119260, SINGAPORE

Contact: matzgy@math.nus.sg