Primal-Dual interior point method for LCP based on a new kernel function with a logarithmic barrier term

Abstract

We consider in this paper , the Primal-Dual Interior Point Method (IPM) for linear Complementarity Problem LCP, based on a new kernel function with a logarithmic barrier term. Furthermore, we suggest an approach, to search direction and proximity utilizing this function. We also demonstrate that the algorithm we employ, exhibits an iteration bound of  $\mathbf{O}\left( qmn^{\frac{mq+1}{2mq}}\log \left( \frac{n}{%\epsilon }\right) \right) $  for large-update. Finally, several numerical problems with the new suggested kernel function's practical performance is reported.