拟线性椭圆变分不等式的障碍最优控制问题  

Optimal Control of Quasilinear Elliptic Obstacle Problems

作　　者：陈启宏[1] 叶玉全[1] 

机构地区：[1]上海财经大学应用数学系,上海200433

出　　处：《数学年刊（A辑）》2006年第5期675-688,共14页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10171030;No.10171059);全国优秀博士学位论文作者专项基金(No.200218)资助的项目

摘　　要：对拟线性椭圆变分不等式的障碍最优控制问题(即以障碍为控制变量)进行了研究．指标泛函为Lagrange型,其中含有控制变量二阶导数的p次幂,这使得最优性条件的推导颇为不易．对所考虑的问题给出了最优控制的存在性定理以及必要条件．This paper considers an optimal control problem for a quasilinear elliptic obstacle variational inequality in which the obstacle is taken as the control. The cost functional of this optimal control problem is of Lagrange type in which the p-th power of Laplacian of the control appears. This feature leads that it is hard to derive the optimality system for the underlying problem. And the existence and optimality system for the optimal control are established.

关 键 词：障碍最优控制问题 存在性 必要条件 

分 类 号：O232[理学—运筹学与控制论]