This constraint only has two variables: Sk,j[n] and qj[n].
I have no idea how to write the above convex constraint legally.
Thanks in advance
The first constraint can be handled by usinglog_sum_exp in the first approach in section 5.2.7 Log-sum-inv of 5 Exponential cone optimization — MOSEK Modeling Cookbook 3.3.0, and making the adjustment for log2 instead of log.
The second constraint appears to be affine. Therefore, can be entered in CVX “as is”.
I’m not clear what the third constraint is. I see “definitional” equality, so I don’t know what the actual constraint is. If that is an equality constraint, it would be non-convex due to the nonlinearity with respect to q_j[n].