A global and local superlinear continuation-smoothing method for P₀and R₀NCP or monotone NCP

We propose a continuation method for a class of nonlinear complementarity problems (NCPs), including the NCP with a P0and R0function and the monotone NCP with a feasible interior point. The continuation method is based on a class of Chen-Mangasarian smoothing functions. Unlike many existing continuation methods, the method follows noninterior smoothing paths, and, as a result, initial points can be easily constructed. In addition, we introduce a procedure dynamically update the neighborhoods associated with the smoothing paths, so that the algorithm is both globally convergent and locally superlinearly convergent under suitable assumptions. Finally, a hybrid continuation-smoothing method is proposed and is shown to have the same convergence properties under weaker conditions.