A self-adjusting interior point algorithm for linear complementarity problems

Based on the min-max principle, the standard centering equation in the interior point method is replaced by the optimality condition of a new proximity measure function. Thus, a self-adjusting mechanism is constructed in the new perturbed system. The Newton direction can be adjusted self-adaptively according to the information of last iterates. A self-adjusting interior point method is given based on the new perturbed system. Numerical comparison is made between this algorithm and a primal-dual interior point algorithm using “standard” perturbed system. Results demonstrate the efficiency and some advantages of the proposed algorithm.