Root relaxation: unbounded when I use cvx with gurobi

If you have binary plus exponential cone (log), I think the only options in CVX are to use Mosek as solver (preferred) or CVXQUAD + Mosek or Gurobi (not preferred).

To use CVXQUAD, see CVXQUAD: How to use CVXQUAD's Pade Approximant instead of CVX's unreliable Successive Approximation for GP mode, log, exp, entr, rel_entr, kl_div, log_det, det_rootn, exponential cone. CVXQUAD's Quantum (Matrix) Entropy & Matrix Log related functions .

As for help with understanding Gurobi Sub-optimal termination, Root relaxation unbounded, perhaps you can get help at https://support.gurobi.com/hc/en-us/community/topics .