基于边界元的分布参数最优控制共轭梯度算法

Conjugate gradient algorithm based on boundary element method to distributed elliptic optimal control problem

得到椭圆型分布参数最优控制问题对应的最优性方程组,在凸性条件下,证明了最优控制的唯一存在性问题．利用一阶最优性条件构造了基于边界元法的共轭梯度算法,给出算法的局部误差估计．最后,以算例验证算法的有效性．

A system of optimality equations of distributed elliptic optimal control problem is derived and, in the convex condition, the existence of a unique solution to optimal control problem is proved. The conjugate gradient algorithm based on boundary element method is developed by means of the associated first-order necessary optimality condition and the local error estimates for this scheme is obtained. Finally, a numerical example is given to illustrate the efficiency of the proposed methodology.