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 using`log_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].