Abstract
In this paper, we consider the numerical method for an optimal control problem governed by an obstacle problem. An approximate optimization problem is proposed by regularizing the original non-differentiable constrained problem with a simple method. The connection between the two formulations is established through some convergence results. A sufficient condition is derived to decide whether a solution of the first-order optimality system is a global minimum. The method with a second-order in time dissipative system is developed to solve the optimality system numerically. Several numerical examples are reported to show the effectiveness of the proposed method.
| Original language | English |
|---|---|
| Pages (from-to) | 577-594 |
| Number of pages | 18 |
| Journal | Journal of Inverse and Ill-Posed Problems |
| Volume | 31 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 1 Aug 2023 |
Keywords
- Optimal control
- dynamical functional particle method
- dynamical system
- global minimum
- obstacle problem
- regularization
- variational inequality