An algorithm for a class of nonlinear complementarity problems with non-Lipschitzian functions |
| |
| Affiliation: | 1. College of Mathematics and Statistics, Chongqing University, Chongqing 400044, PR China;2. School of Mathematical Sciences, Chongqing Normal University, Chongqing 400047, PR China;3. Key Laboratory for Optimization and Control Ministry of Education, Chongqing Normal University, Chongqing 400047, PR China;1. School of Mathematical Sciences, Chongqing Normal University, Chongqing 400047, PR China;2. College of Mathematics and Statistics, Chongqing University, Chongqing 400044, PR China;1. School of Mathematical Sciences, Chongqing Normal University, Chongqing 400047, PR China;2. Key Laboratory for Optimization and Control Ministry of Education, Chongqing Normal University, Chongqing 400047, PR China |
| |
| Abstract: | In this paper, we focus on solving a class of nonlinear complementarity problems with non-Lipschitzian functions. We first introduce a generalized class of smoothing functions for the plus function. By combining it with Robinson's normal equation, we reformulate the complementarity problem as a family of parameterized smoothing equations. Then, a smoothing Newton method combined with a new nonmonotone line search scheme is employed to compute a solution of the smoothing equations. The global and local superlinear convergence of the proposed method is proved under mild assumptions. Preliminary numerical results obtained applying the proposed approach to nonlinear complementarity problems arising in free boundary problems are reported. They show that the smoothing function and the nonmonotone line search scheme proposed in this paper are effective. |
| |
| Keywords: | Nonlinear complementarity problem Free boundary problem Smoothing Newton method Local superlinear convergence |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
