convex >= constant is a non-convex constraint; therefore, not allowed by CVX. If you want abs(cvx variable) >= constant, you would need to introduce binary variables to handle this non-convex use of the convex function abs. You can search at https://or.stackexchange.com/ and ask for help there on how to do that. You will need to have Gutobi or Mosek available as solver to do this in CVX.