解互补问题的一类广义拟牛顿算法

A Class of Generalized Quasi-Newton Methods for Solving Complementarity Problems

互补问题在实际生活中有着广泛的应用,是当前研究的一个热点问题,从而产生了很多的解决途径。本文利用互补函数将互补问题转化为一个无约束最优化问题,从而构造了一类求解互补问题的广义拟牛顿算法,并从理论上给出了无约束最优化问题的解是原互补问题解的一个充分条件。数值实验表明算法不仅可行而且效果较好。

Complementarity problem has been the hotspot in the research of mathematical programming and many methods have been proposed.In this paper,complementarity problem is convert into unconstrained optimization by using complementarity function.It is also proved that the solution of unconstrained optimization is that of the complemetarity problems.Numerical experiments indicate that the new method is feasible and efficient.