A Conjugate Gradient Algorithm for General Linear Elliptic Optimal Control Problems

本文针对一类一般线性椭圆最优控制问题，应用了一种带有强Wolfe-Powell准则的共轭梯度算法对其进行求解，并从理论上分析了带有强Wolfe-Powell准则的共轭梯度算法的可行性以及全局收敛性。最后，我们做了相应的数值实验去验证算法的有效性。In this paper, we investigate a class of general linear elliptic optimal control problems. The conjugate gradient method with strong Wolfe-Powell criterion is used to solve this research problem. The feasibility and global convergence of conjugate gradient method with strong Wolfe-Powell criterion is theoretically proved. Finally, we do the corresponding numerical experiments to verify the feasibility of algorithm.