Need a help to formulate an optimization problem?

I need help in formulating an optimisation problem which is briefed here.

alpha and beta are weighting parameters and scalars (0.1 and 100 soemthing like this)

Decision variable :

where,

Since is hidden and not at all visible in the optimisation function, I am struggling to set the constraints and formulating them.

I need a first hand advice to build the algorithm, (actually "where to start with") and some other examples that I should refer, so I can get an idea how to formulate the problem.

I went through the examples given in MATLAB, and I think they are not that much advanced enough.

Thanks.