Convert the perspective function of log-sum-exp to cvx

Is t constrained to be >= 0? Presuming it is, you can look at Convert problem to cvx which I think will let you handle (28a) and (28b).

I don’t know the values of your input data, but you have not yet convinced me that (28c) and (28d) are convex. Can you do so? That is your responsibility per the “rules” of the forum.