I want to solve this convex problem using cvx, but cvx failed, can you help me? is this problem too complex?

The problem status is ill_posed, then search this on this forum

ok,thank you
but i don’t know how to modified my model.can you help me?

It is unlikely anyone has the time and/or willingness to help you on this issue.

You to have understand what ill-posed means and then figure out why your problem is ill-posed.

Did you skip the first line of output from CVX? It might say that is it solving the dual. if so, Mosek saying the problem is primal ill-posed means the original problem is dual ill-posed. Perhaps the feasible region has no relative interior, and to remove this ill-posedness, you need to redefine variables and constraints to be in a lower dimensional space in which there would be a relative interior.

ok,thank you very much will try again

this constraint is based on taylor expansion, F1_ini and F2_ini are given points, i think this is the reason why the optimization problem is ill-posed

Are you showing us the code you actually ran? That constraint appears to have log_det, which is concave, on the LHS of <= constraint. That would be a non-convex constraint. so I think this should not be accepted by CVX. But it apparently was. Am I misreading the constraint?

thank you very much for reading my code, thank you very much

Your code keeps changing. We don’t know what goes with what. Your code deoes not have all the input data, so forum readers can’t run it.

Your last post has cvx_precision best. Do not use that. Stick with the default.

I still don’t know why log_det(...) <= ... is accepted by CVX, if it actually is accepted.

Declaration of sdp mode doesn’t do anything in your code (but doesn’t do any harm), because you don’t use <= or >= to define semidefinite constraints.

ok,thank you very much

in the second constrain, F1_ini and F2_ini are constant matrix, optimal variable are F1,F2, so the second constraint is convex.

O.k., so log_det is a constant, and the constraint is affine. That resolves that mystery.

Do the equality constraints collectively constrain away the interior of the semidefinite (including log_det) constraints? Perhaps you could investigate this by changing semidefinite constraints to F1 >= 1e-4*eye(bs_antenna_number) and similarly with F2 and see whether the problem is still feasible. I’m not sure whether something should also be done with the log_det constraint. But if the modification of the semidefinite constraints results in infeasible, that suggests the lack of ability to satisfy the semidefintie constraints as strict enough definite constraints, might constitute iill-posedness of your problem formulation (Slater condition, which Mosek and other solvers rely on, not satisfied).

hello, is this warning tells me something cause the ill-posed situation?

You keep changing the problem. Now you have log(cvx_expression), so CVX’s unreliable successive approximation method was used because you specified sedumi as solver. You should instead use Mosek as solver, which will use Mosek’s native exponential cone capability, which is much more reliable, and likely faster.

ok thank you very much