逆混合变分不等式的弱尖锐性

Weak sharp minima for inverse mixed variational inequalities

利用KKM定理(Knaster-Kuratowski-Mazurkiewicz定理),得到Banach空间中广义逆混合变分不等式解的存在性.提出高阶弱尖锐性的概念,探讨Banach空间中原间隙函数与弱尖锐性的联系,利用可微性、法准和近似对偶映射,得到弱尖锐性存在的2个充分和必要条件.

By KKM theorem,we obtain the existence of solutions to inverse mixed variational inequalities in Banach spaces.We introduce the concept of high-order weak sharp minima.Then we discuss the relationship between the original gap function and weak sharp minima in Banach spaces.By using differentiability,normal cones and approximate dual mappings,several sufficient and necessary conditions for the existence of weak sharp minima are obtained.