对于不可微的“极大值”形式的函数,可以利用凝聚函数对其进行光滑逼近.借助这个技术,给出了求解线性互补问题的光滑方程组算法.首先是将互补问题转化为等价的非光滑方程组,再利用凝聚函数进行光滑逼近,从而转化为光滑方程组的求解问题.通过一些考题对这个算法进行了数值试验,结果显示了该算法的有效性和稳定性.
The undifferentiable "max" function can be approximated by a differentiable aggregate function. Based on this technique, a smoothing equation algorithm for solving linear complementarity problems is presented in this paper. The linear complementarity problems can be reformulated as a system of nonsmooth equations. A smoothing approximation to the nonsmooth equations is given by the aggregate function. Then a smoothing equation algorithm is developed. The reliability and efficiency of the algorithm is demonstrated by numerical experiments.