I have a constraint, that I am unable to write in CVX acceptable syntax. Help!

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Based on Mark’s analysis I’m going to suggest that even if it is convex for the chosen parameters, it cannot be represented in CVX. See the following similar models:

x\log(1+1/x) using CVX

How to implement following function \sum\limits_i {\sum\limits_k {{y_i}\log (1 + \frac{{x_i^k}}{{{y_i}}})} }

CVX simply cannot handle arbitrary convex functions, even if they are differentiable. If a model cannot be represented by the functions listed in the reference guide, then CVX cannot handle it. Any new functions we add will actually be represented by the existing list. This is due to the very specific way CVX translates and solves models, and due to the limitations of the underlying solvers.