A new active-set strategy for NCP with degenerate solutions

In this paper, we present a semismooth Newton-type method for solving nonlinear complementarity problems with degenerate solutions. At each iteration, an estimated set is used to approximate the degenerate indices of the solutions. Then, a judge step is introduced to decide whether a standard Newton step or a reduced Newton step will be executed. The method combines the standard step and the reduced step in one algorithm. The standard Newton step is mainly used to keep the rate of the global convergence. When near the solution, the degenerate indices will be correctly identified and the original problem will be transformed to a reduced non-degenerate problem. Under some mild assumptions, local superlinear convergence is obtained.