函数空间中总极值的R-收敛有限维逼近  

Finite Dimensional Approximation to Global Minimizers in Functional Spaces With R-Convergence

作　　者：陈熙[1] 姚奕荣[1] 郑权[1,2] 

机构地区：[1]上海大学理学院数学系,上海200444 [2]哥伦布州立大学数学系

出　　处：《应用数学和力学》2011年第1期103-112,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10771158);上海市重点学科资助项目(S30104)

摘　　要：应用测度序列R-收敛的新概念来描述函数空间中总极值问题解的有限维逼近,并利用变差积分途径来寻找这样的解.针对有约束问题,运用罚变差积分算法把所给问题转化为无约束问题,且给出一个非凸状态约束最优控制问题的数值例子以说明该算法的有效性.New concept of convergence （ R-convergence） of a sequence of measures was applied to characterize global minimizers in functional space as a sequence of approximating solutions in finite-dimensional spaces. A deviation integral approach was used to find such solutions. For a constrained problem,a penalized deviation integral algorithm was proposed to convert it to unconstrained ones. A numerical example on optimal control problem with non convex state constrains was given to show that the algorithm is efficient.

关 键 词：总极值 变差积分 变测度 R-收敛 有限维逼近 

分 类 号：O224[理学—运筹学与控制论]