My simulation results are inconsistent with my expectation

[Mark_L_Stone]

It’s your model. I don’t think you can expect CVX forum readers to understand how to model whatever it is you are modeling.

Moreover, between poorly scaled input data and use of SCA, we have no idea whether SCA is converging to anything lest alone a global or even local optimum of your original problem.

The comments I provided to your earlier questions also apply to this question.

Why these variables are optimized to zero?

I don’t sufficiently understand your model to have an opinion as to whether your opinion is correct. But if your opinion is correct, can you produce values of the variables which your opinion says should exist, and which produce a better objective value. If not, perhaps your model is not suited for your purpose, and you need to figure out how to change it to make it so.

Algorithm cannot converge

SCA is generally unreliable, and might not converge to anything, let alone a global or even local optimum of the original problem. You should try to improve numerical scaling of input data, for instance by changing units, so that all non-zero input data is within a small number of orders of magnitude of 1. That might help your overall SCA performance, but not necessarily. Different (better) initialization values for the “SCA” variables might help, but not necessarily.