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

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.