Article ID: | iaor20163926 |
Volume: | 37 |
Issue: | 6 |
Start Page Number: | 1314 |
End Page Number: | 1328 |
Publication Date: | Nov 2016 |
Journal: | Optimal Control Applications and Methods |
Authors: | Yu Yang, Luo Xiaochuan, Wang Yuan, Cui Haijuan |
Keywords: | optimization, engineering |
Our work is devoted to an optimal control problem for two‐dimensional parabolic partial differential equations(PDEs) and its application in engineering sciences. An adjoint problem approach is used for analysis of the Fréchet gradient of the cost functional, and we prove the gradient is Lipschitz continuous. An improved conjugate gradient method is proposed to solve this problem. Based on Lipschitz continuity of the gradient, the convergence analysis of the conjugate gradient algorithm we proposed is studied. Results of some computational experiments obtained by the conjugate gradient algorithm are illustrated. The results show that the improved conjugate gradient algorithm is effective