Need help to reformulate Projectile Motion to a convex problem

I have no idea what your formula
vx * vy * 2/ g
i s supposed to be. What is that the maximum distance of? I certainly don’t see such a formula anywhere in the Wikipedia article you linked.

vx * vy * 2/ g is neither a convex nor concave function of vx and vy. If vx is fixed at a particular value, such as 10, rather than being a CVX variable, then vx * vy * 2/ g is an affine function of vy. As such, CVX will allow you to use it in an objective function to be maximized or minimized, or on the Left Hand Side or Right Hand Side of an equality or inequality constraint.

Perhaps you were referring to Why isn't CVX accepting my model? READ THIS FIRST! ? Please read it carefully and follow its sagacious advice.