有界约束单调变分不等式的内点连续算法

An interior-point continuation method for monotone variational inequalities with box constraint

讨论变分不等式问题 VIP( X,F) ,其中 F是单调函数 ,约束集 X为有界区域 .利用摄动技术和一类光滑互补函数将问题等价转化为序列含两个参数的非线性方程组 ,然后据此建立 VIP( X,F)的一个内点连续算法 .分析和论证了方程组解的存在性和惟一性等重要性质 ,证明了算法很好的整体收敛性 。

This paper studies VIP( X,F) ,where F is a monotone function and constraint set X has the form of box constraint.By means of perturbation technique and a type of smooth complementarity function,at first the problem is equivalently transformed into a sequential system of nonlinear equations with two parameters and then an interior\|point continuation method is established.Secondly,some important properties of the system of equations such as existence and uniqueness of solution are analysed and discussed.At the same time,the global convergence of proposed algorithm is also proved.Finally,some preliminary numerical results are reported.$$$$