一类混合逆变分不等式的间隙函数和误差界

A Study of MIVI Gap Function and Error Bounds

在Hilbert中研究了一类混合逆变分不等式(简称MIVI)。MIVI分别构造了四类间隙函数,分别是自然残差函数、间隙函数、正则间隙函数、D-间隙函数。并且在强单调和Lipschitz连续的条件下分别得到了不同的误差界。证明过程主要借用了广义f-投影算子,它是近似算子的一种推广。

In this study,a mixed inverse variational inequality（MIVI） is studied in Hilbert spaces. Four merit functions for MIVI are proposed,that is,the natural residual,gap function,regularized gap function and D-gap function. And by using these functions,error bounds are obtained,i.e.,upper estimates for the distance to solutions of MIVI.The approach used in this study is based on the generalized f-projection operator,but not the proximal mapping.