How to solve z<=x/y^4 in cvx?

In my constraint, z<=x/y^4. x,y,z are variables. z is convex. x/y^4 is concave. convex<=convex should not be Taylor expansion. But CVX does not allow three variables in one I try to use ln(). lnz< I use Taylor expansion to solve this problem. But Z always appears negative which leads to infeasible. So what should I do?

x/y^4 is neither convex nor concave, even at such seemingly nice values as x = y = 1. So CVX is not the right tool for this. if you insist on using such ad hoc methods as Tayor series, you can’t expect that will result in successful solving of your original problem, and you’re on your own. You could instead use YALMIP, from which non-convex solvers can be called.