On the convergence rate of Newton interior-point methods in the absence of strict complementarity

In the absence of strict complementarity, Monteiro and Wright proved that the convergence rate for a class of Newton interior-point methods for linear complementarity problems is at best linear. They also established an upper bound of 1/4 for the Q1-factor of the duality gap sequence when the steplengths converge to one. In the current paper, we prove that the Q1 factor of the duality gap sequence is exactly 1/4. In addition, the convergence of the Tapia indicators is also discussed.