Have you proven the optimization problem is convex? How did you do so?
The forum readers can’t determine from your preceding post whether the problem is convex, because sufficient information is not provided in it. We don’t know what all those symbols mean, and which of them might have some unstated relation to the listed optimization variables.
We don’t know the value of \alpha. If 0 < \alpha <= 2, then u^{2/\alpha} is concave, and rhe 2nd constraint is convex, and can be entered as is, presuming the LHS is constant (which I don’t know, because I don’t know what those symbols are).
Please carefully read
Edit: corrected typo to 0 < \alpha <= 2.