求解一类变分不等式问题的信赖域算法

变分不等式作为变分原理的主要推广,是数学上的一个主要分支.近年来,变分不等式理论已被大量应用于经济与金融、交通各个领域中.将一类变分不等式问题等价转化为无约束优化问题,并提出了一个求解无约束优化问题的信赖域算法;在通常假设下,证明了算法的全局收敛性.该算法可用于网络的均衡模型,使得模型解的精确程度有了很大地提高.

Trust region algorithm for solving a class of variational inequality problems

As the extension of variational theory,the variational inequality is an important branch of mathematics,which has been used in many fields such as economics,finance and transportation in recent years.The variational inequality problems were equivalently transformed into general unconstrained optimization problems.Then,a trust regional gorithm was proposed to solve the unconstrained optimization problems.Under mild conditions,the global convergence of the algorithm was proved.This method can be used to impro...