具有广义多面体约束的参数变分不等式解映射伴同导数

摘要

在研究参数变分不等式稳定性理论及均衡约束数学规划的最优性条件时，计算参数变分不等式解映射的伴同导数显得尤为重要。考虑了具有等式约束的广义多面体约束的参数不等式。首先，在无约束规范条件下，利用二阶微分理论，给出了具有广义多面体约束的法锥的图的法锥。其次，借助辅助多面体集合及约束规范条件，得到了更为简洁的法锥形式。最后，给出参数变分不等式的解映射的伴同导数。%It is of great importance to compute the coderivative of the solution mapping to the parametric variational inequality while investigating the stability theory of the parametric variational inequality and optimality conditions of the mathematical programming governed by equilibrium constraints. A class of parametric variational inequalities constrained by generalized polyhedra including the equality constraints is considered.Firstly,by virtue of the second-order differentiation theory,the normal cone is given to graph of the normal cone constrained by generalized polyhedra without any constraint qualifications.Next,under the auxiliary polyhedral set and the provided constraint qualification,the formula of the above-obtained normal cone is simplified.Finally,the coderivative of the solution mapping to the parametric variational inequality is given.