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中文摘要：
提出一种新的QP-free方法解变分不等式问题.通过光滑化的Fischer-Burmeister函数,把变分不等式的KKT优化条件转换为一个简单的约束优化问题,并给出了解这个约束优化问题的迭代算法.这个方法的主要优点是：①能够解任意的变分不等式问题;②每步迭代只需解一个线性方程组;③算法是全局收敛的,在一定条件下是超线性收敛的.数值试验结果表明,这个算法是有效的.
英文摘要：
A new QP-free method is proposed for the solution of variational inequalities problem. By the smoothing Fischer-Burmeister functions, a simple constrained optimization reformulation of the KKT optimality conditions is derived from variational inequalities. Based on the reformulation, an iterative method is presented. The main properties of this method are： It is well defined for an arbitrary variational inequalities problem; it has to solve just one linear system of equations at each iteration; it is globally convergent; and it is locally superlinerly convergent under certain conditions. Preliminary numerical results indicate that this method is quite promising.
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