Control Problem with Sum of Squares Cost

[aarraf]

Hi,

is there an implementation available to solve optimal control problems with the Sum of Squares cost?
Basically as in Tutorial 06, case 1a: Poisson problem with distributed control but with $y_d$ defined at a set of points instead of FE-Space.

Thanks in Advance.

[francesco-ballarin]

I am not aware of anyone who has worked on this. I have not calculate the optimality conditions for this case, but I guess you'll have some point sources in the adjoint. If so, another dolfinx-based library named scifem may be helpful https://github.com/scientificcomputing/scifem/blob/main/examples/point_source.py , but it would be up to you to determine how to combine that with multiphenicsx

[aarraf]

Thanks for your reply.
Your right, in this case the adjoint includes point sources at the sensor locations. And thanks for referring the scifem, I will check that out.