Equality constraints make solution infeasible

[Brett Hannigan]

I am using YALMIP to solve a linear matrix inequality problem with an equality constraint. The equality constraint is of the form A + B*X*C = 0 where A, B, C are constant matrices and X is a matrix variable. If I set up the problem where I directly solve for X = -B^-1*A*C^-1, then use it in the other inequalities as a constant, the linear matrix inequality is feasible. If I do not solve for X and add it as an equality constraint in YALMIP, the SDP problem is infeasible. Is this expected behaviour? If this is a solver issue, I have tried it with SDPT3 and SeDuMi with the same results.

Thanks in advance, 

Brett

[Johan Löfberg]

My guess is X is symmetric

https://yalmip.github.io/tutorial/basics/

[Brett Hannigan]

Good thought, but I defined X as full:

X = sdpvar(nu, ny, 'full')

[Johan Löfberg]

then it makes no sense, and can only be answered if you supply data and code

[Rayza Araújo]

Hi!

I am actually having this same issue. I have some LMI problem that is feasible and gives me an answer. When I add the equality contraint to calculate the eigenvalue of a matrix, it results in infeasible. I am fowarding the code to you, it uses yalmip and sedumi. I created a section called "%% If I uncomment this part, its not feasible" to make it easier to understand. But if something is not clear, feel free to ask. I am sure what's causing this is silly, but I have stared at this script for so long I can't even see it anymore. 

Thaks in advance!

[Rayza Araújo]

Oops, I forgot to comment line 169. Here's the updated version.