非线性互补问题的光滑算法

A Smoothing Algorithm for Nonlinear Complementarity Problems

基于非线性互补问题(NCP(F))的等价变形,利用Fischer-Burmeister函数的光滑逼近函数将非线性互补问题转化为优化问题。提出了一种求解非线性互补问题的光滑逼近算法,通过构造非线性互补问题的一个新的光滑逼近函数,将非线性互补问题等价地转化为求解光滑方程组问题。在一定条件下证明了该算法的全局收敛性。数值实验结果说明了算法的有效性。

Based on the equivalent deformation of nonlinear complementarity problems（NCP（F）） and the use of smooth approximating functions of Fischer-Burmeister function,the problem is transformed into optimization problem. A smoothing approximation algorithm is proposed for solving the nonlinear complementarity problem.By introducing a new smoothing NCP-function,the problem is approximated by a family of parameterized smooth equations. The proposed algorithm has been proved to be globally convergent under certain conditions. Numerical experiment results demonstrate the effectiveness of the algorithm.