An $O(\sqrt{n}L)$ iteration Mehrotra-type predictor-corrector algorithm for monotone linear complementarity problem

Abstract

In this paper we propose a new class of Mehrotra-type predictor-corrector algorithm for the monotone linear complementarity problems (LCPs). At each iteration, the method computes a corrector direction in addition to the Ai–Zhang direction (SIAM J Optim 16:400–417, 2005), in an attempt to improve performance. Starting with a feasible point $(x^0, s^0)$ in the wide neighborhood $\mathcal {N}(\tau ,\beta )$, the algorithm enjoys the low iteration bound of $O(\sqrt{n}L)$, where $n$ is the dimension of the problem and $L=\log \frac{(x^0)^T s^0}{\varepsilon }$ with $\varepsilon$ the required precision. We also prove that the new algorithm can be specified into an easy implementable variant for solving the monotone LCPs, in such a way that the iteration bound is still $O(\sqrt{n}L)$. Some preliminary numerical results are provided as well.