| Article ID: | iaor201112244 |
| Volume: | 32 |
| Issue: | 6 |
| Start Page Number: | 734 |
| End Page Number: | 747 |
| Publication Date: | Nov 2011 |
| Journal: | Optimal Control Applications and Methods |
| Authors: | Luan Shu, Gao Hang, Li Xiaopei |
| Keywords: | optimization, heuristics |
An optimal control problem governed by a class of semilinear non-well-posed elliptic equations is discussed in this paper. It is pointed out that the state equation we considered has exactly two solutions and the control domain and cost functional maybe non-convex. Using the relaxed controls, Pontryagin's maximum principle for the optimal pairs is obtained.