有限维逼近无限维总极值的水平值估计方法  

Finite Dimensional Approximation to Global Minima:A Level-Value Estimation Method

作　　者：陈晓方[1] 楼烨[1,2] 张海东[1] 

机构地区：[1]上海大学数学系,上海200444 [2]上海科技学院,上海201800

出　　处：《应用数学与计算数学学报》2010年第1期1-8,共8页Communication on Applied Mathematics and Computation

基　　金：上海市重点学科(S30104)建设项目;上海自然科学基金(09ZR1411100)资助

摘　　要：变分计算、最优控制、微分对策等常常要求考虑无限维空间中的总极值问题,但实际计算中只能得出有限维空间中的解.本文用有限维逼近无限维的方法来讨论函数空间中的总体最优化问题.用水平值估计和变侧度方法来求得有限维逼近总体最优化问题.对于有约束问题,用不连续精确罚函数法将其转化为无约束问题求解.It is required to consider global minimization problems in infinite dimensional spaces in calculus of variations,optimal control and differential games.However, in practical computation one can only find solutions in finite dimensional spaces.New optimality of the integral global minimization are applied to characterize global minimun in functional space as a sequence of approximating solutions in finite-dimensional spaces. A variable measure algorithm and a level-value estimation method are used to find the solutions in finite-dimensional spaces.For a constrained problem,a discontinuous penalty method is proposed to convert it into a unconstrained problem.

关 键 词：有限维逼近 变侧度方法 水平值估计 

分 类 号：O224[理学—运筹学与控制论]