Abstract
We propose an alternating direction method of multipliers (ADMM) for solving the state constrained optimization problems governed by elliptic equations. The unconstrained as well as box-constrained cases of the Dirichlet boundary control, Robin boundary control, and right-hand side control problems are considered here. These continuous optimization problems are transformed into discrete optimization problems by the finite element method discretization, then are solved by ADMM. The ADMM is an efficient first order algorithm with global convergence, which combines the decomposability of dual ascent with the superior convergence properties of the method of multipliers. We shall present exhaustive convergence analysis of ADMM for these different type optimization problems. The numerical experiments are performed to verify the efficiency of the method. © 2016, Science China Press and Springer-Verlag Berlin Heidelberg.
| Original language | English |
|---|---|
| Pages (from-to) | 361-378 |
| Journal | Science China Mathematics |
| Volume | 60 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1 Feb 2017 |
| Externally published | Yes |
Bibliographical note
Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].Research Keywords
- ADMM
- elliptic equation constrained
- optimal control problems