半线性椭圆方程在非凸容许控制集上最优问题的二阶分析  

Second-order anylysis of optimal problem of semilinear elliptic equations on non-convex control set

作　　者：赵东红[1] 陶理[1] 

机构地区：[1]东北师范大学数学系,吉林长春130024

出　　处：《东北师大学报（自然科学版）》2002年第4期1-7,共7页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10071012)

摘　　要：　给出了半线性椭圆方程在非凸容许控制集上最优控制问题的二阶分析,主要创新在于控制集合是非凸集,需要对控制函数做"针状变分",得到二阶必要条件,重新讨论目标泛函J(u)的二阶泰勒展开式,因此上述问题变得更加精细并有意义.In this paper,concerned with some optimal control problems governed by semilinear elliptic equations.One-order necessary conditions of optimal control problems have been studied very fully.Relatively,for partial defferential equation,second-order necessary conditions of optimal control problems have been studied.Moreover,the control set selected by them is convex.The main difference in this paper is non-convex on the control.In this case,in order to obtain second-order necessary conditions,need to discuss second-order Tayler expansion of cost function again,so this makes the problems interesting and delicate.

关 键 词：半线性椭圆方程 非凸容许控制集 二阶分析 最优控制 针状变分 二阶必要条件 

分 类 号：O232[理学—运筹学与控制论] O175.25[理学—数学]