一类参数拟变分不等式解映射的伴同导数  

Coderivatives of solution map to a parametric quasi-variational inequality

作　　者：张杰[1,2] 任咏红[2] 张立卫[1] 

机构地区：[1]大连理工大学数学科学学院,辽宁大连116024 [2]辽宁师范大学数学学院,辽宁大连116029

出　　处：《大连理工大学学报》2012年第4期619-624,共6页Journal of Dalian University of Technology

基　　金：辽宁省博士科研启动基金资助项目(20091046);国家自然科学基金资助项目(11071029)

摘　　要：由Mordukhovich准则可知,伴同导数是研究解映射类Lipschitz性质的主要工具,所以研究参数拟变分不等式的解映射的伴同导数具有重要的理论意义.主要研究了一类等式和不等式约束的参数拟变分不等式的解映射的伴同导数的估计式.首先在某些平稳性条件下,通过法锥的具体表达形式给出了参数拟变分不等式的解映射的伴同导数的指标形式表达的估计式,然后在数学规划常用的约束规范下,建立了伴同导数等于其估计式的充分条件.所得的结果完善了已有的一个伴同导数表示定理.According to Mordukhovich criterion, the coderivative is the main tool to study the Lipschitz-like property of solution map, so it is theoretical valuable to study coderivatives of solution maps to parametric quasi-variational inequalities. The estimate formula of coderivative of solution map to an equality and inequality constrained par under some calmness conditions, by the ametric quasi-variational inequality is studied. At first, description of normal cone, the estimate formula of coderivative of parametric quasi-variational inequality in the index sets style is obtained. Furthermore, under some constraint qualifications of mathematical programming, the sufficient condition ensuring the equality of coderivative and its estimate formula is established. The results obtained can be seen as a supplement to a coderivative description theorem.

关 键 词：参数拟变分不等式 解映射 伴同导数 

分 类 号：O221.2[理学—运筹学与控制论]