The first step is for you to formulate the problem explicitly in terms of optimization variables (C_x?) and input data (everything else, including all the derivatives?). Are there unstated relationships between any of these things? Why is the objective written as a function of \zeta? If \zeta is fixed, what s the meaning of any of this, and if it is a variable, what is it related to? Or things are a function of \zeta, differentiated with respect to \zeta, and then the value of \zeta is fixed at some particular value to evaluate this, rendering everything other than C_x as numerical input data? I don’t understand any of that. Hopefully you do, and if not, will more carefully study whatever paper or book this comes from, if not your own.
The next step is for you to prove this is a convex optimization problem, which looks very doubtful to me.