New smoothing methods for solving the linear complementarity problem with P0-matrix

Based on smoothing techniques, we propose two new methods to solve linear complementarity problems (LCP) called TLCP and Soft-LCP. The idea of these two new methods takes inspiration from interior-point methods in optimization. The technique that we propose avoids any parameter management while ensuring good theoretical convergence results. In our approach, we do not need any complicated strategy to update the smoothing parameter r since we will consider it as a new variable. Our methods are validated by extensive numerical tests, in which we compare our methods to several other classical methods