A Global Linear and Local Quadratic Noninterior Continuation Method for Nonlinear Complementarity Problems Based on Chen-Mangasarian Smoothing Functions

摘要

A noninterior continuation method is proposed for nonlinear complementarity problems. It improves the noninterior continuation methods recently studied by Burke and Xu [Math. Oper. Res., 23 (1998), pp. 719-734] and Xu [The Global Linear convergence of an Infeasible Non-Interior Path-following Algorithm for complementarity Problems with Uniform P-functions, Preprint, Department of Mathematics, University of Washington, Seattle, 1996]; the interior point neighborhood technique is extended to a broader class of smoothing functions introduced by Chen and Mangasarian [Comput. Optim. Appl., 5 (1996), pp. 97-138]. The method is shown to be globally linearly convergent following the methodology established by Burke and Xu. In addition, a local acceleration step is added to the method so that it is also locally quadratically convergent under suitable assumptions.