Improved smoothing Newton methods for \(P_0\) nonlinear complementarity problems (Q732492)

A one-step smoothing Newton method is presented to solve the \(P_0\) nonlinear complementarity problems. The solution can be obtained from any accumulation point of the iteration sequence generated by the algorithm. It does not assume a priori the existence of an accumulation point. The algorithm solves a system of linear equations and performs one line search per iteration. If an accumulation point of the iteration sequence satisfies a nonsingularity assumption then the iteration sequence converges to the accumulation point globally and superlinearly without strict complementarity. If the Jacobian of the objective function is Lipschitz continuous then the iteration sequence converges locally quadratically. An experiment on eight numerical problems is provided to illustrate the performance of the algorithm.