A Quadratically Convergent Polynomial Long - Stepalgorithm for a Class of Nonlinearmonotone Complementarity Problems

Several interior point algorithms have been proposed for solving nonlinear monotone complementarity problems. Some of them have polynomial worst-case complexity but have to connne to short steps, whereas some of the others can take long steps but no polynomial complexity is proven. This paper presents an algorithm which is both long-step and polynomial. In addition, the sequence generated by the algorithm, as well as the corresponding complementarity gap, converges quadratically. The proof of the polynomial complexity requires that the monotone mapping satisses a scaled Lipschitz condition, while the quadratic rate of convergence is derived under the assumptions that the problem has a strictly complementary solution and that the Jacobian of the mapping satisses certain regularity conditions.