That is non-convex, as can easily be seen by example even in one dimension, norm(P) - J), with or without squaring, where P is a scalar variable.
It’s your problem, so you would have to determine what, if any, would be an adequate convex approximation, which would be out of scope for this forum.
If this is the problem you actually want to solve (but you need not have the square the objective function), you could solve it with a non-convex solver,for instance using YALMIP.
In the future, please determine whether a problem is convex before posting, rather than asking the forum readers whether the problem is convex.