A global and local superlinear continuation-smoothing method for P-0 and R-0 NCP or monotone NCP

We propose a continuation method for a class of nonlinear complementarity p roblems (NCPs), including the NCP with a P-0 and R-0 function and the monot one NCP with a feasible interior point. The continuation method is based on a class of Chen-Mangasarian smoothing functions. Unlike many existing cont inuation methods, the method follows noninterior smoothing paths, and, as a result, initial points can be easily constructed. In addition, we introduc e a procedure to dynamically update the neighborhoods associated with the s moothing paths, so that the algorithm is both globally convergent and local ly superlinearly convergent under suitable assumptions. Finally, a hybrid c ontinuation-smoothing method is proposed and is shown to have the same conv ergence properties under weaker conditions.