For the primal problem:
I can solve it and obtain a finite minimum. However, for its dual problem:
The solution is unbounded. I’m confused about this result. Shouldn’t the solution of the dual problem be less than or equal to the solution of the original problem? Thank you！
This is the CVX forum. So to make it on topic, you should show your CVX code, complete with input data, as well as the solver and CVX output.
I presume the \ge are in the semidefinite sense, i.e., \succeq ? Your primal and dual seem to match with (8.13) and (8.14) of The Mosek Modeling Cookbook https://docs.mosek.com/MOSEKModelingCookbook-letter.pdf . Have you properly specified the semidefinite constraints per CVX syntax http://cvxr.com/cvx/doc/sdp.html ?
Ok, thanks. I solved it. I ignored the symmetry of the matrix.