The optimal solution didn't meet the constraints!

[Rong Zhao]

I got my problem successfully solved by using either one of the three different solvers: sdpt3, mosel, sedumi.

The problem can be successfully solve by using either one of the three solvers, however, the solutions I got (matrices and the values) didn't meet the constraints I've set to get these solutions. 

There are 11 constraints in all, and seven of them are satisfied with the solution, but the other 4 cannot be satisfied?

Can anybody help me, thank you  very much!

[Johan Löfberg]

https://yalmip.github.io/faq/solutionviolated/

[Rong Zhao]

Thank you very much for your reply.

I've noticed this possibility for my problem, and I've tried to set more stringent constraints on the conditions that don't meet the requirement, just as what you suggested. 

However, I'm not sure if it is because there are too many constraints (12 in my problem) so there is some kind of coupling, no matter how I adjust the the boundary, the problem still exists.(And it is always the same 4 constraints cannot be satisfied)

Could give me more some suggestions? Is there a possibility that my problem is too special that it just cannot get solved through YALMIP?

[Johan Löfberg]

it's not related to the number of constraints (and 12 constraints is nothing), it's just the way solvers work. they typically approach the optimal point from the exterior, and once it is close enough to feasible it returns the solution

if it persist no matter what you do, then you must be doing something wrong.

if I want to minimize x subject to x>=0, and I get -0.0000001 and I don't like that, if I change the constraint to x>=1 (i.e. a massive margin) there is no chance that it still would return a slightly infeasible solution, it will be at least 0.999999 or something like that. If you still get a slightly infeasible solution, you've either used a too small margin, or you haven't looked at the solver diagnostics to see that it perhaps has told you that it gave up and concluded the problem was infeasible

[Rong Zhao]

I got your point, I'll keep trying to find my real feasible solution, thank you very much for your reply!

[Rong Zhao]

Just as you said, I've got the real solutions, thank you very much, your help is greatly appreciated!