中文摘要：

利用Konnov对变分不等式问题的标量化方法,对一般的强变分不等式（SVI）和弱变分不等式（WVI）进行了进一步的推广.主要介绍了基于集值映射的强广义混合向量变分不等式（SGMVVI）和弱广义混合向量变分不等式（WGMVVI）,考虑了与它们相关的间隙函数,在合适的条件下讨论了强广义混合集值变分不等式（SGMVI）的间隙函数和SGMVVI的间隙函数之间的关系,以及WGMVVI和SGMVI的间隙函数之间的关系,最后讨论了它们的间隙函数的全局误差界.

英文摘要：

The Konnov scalarization method for variational inequality problems was used to further generalize the classical strongly variational inequalities （SVIs） and the classical weakly variational inequalities （WVIs）. The strongly generalized mixed vector variational inequalities （ SGMVVIs） and the weakly generalized mixed vector variational inequalities （WGMVVIs） were studied based on set-valued mappings in view of their gap functions. Under proper conditions, the relationship between the gap function of the strongly generalized mixed set-valued variational inequality （SGMVI） and that of the SGMVVI, and the relationship between the gap functions of the WGMVVI and the SGMVI, were discussed. At last, the global error bounds of the gap functions were obtained.