Was a quotient of two norms considered as a constraint to a convex optimization problem before?

I want to solve the optimization problem
text{minimize }g(x) quad text{subject to} quad Vert xVert_{infty}/Vert xVert_{2} le s

for $xinmathbb{R}^d$ and $sin(0,infty)$.
The function $g$ is (strongly) convex and Lipschitz smooth.

I know, that I could probably try to find saddle points of the corresponding Lagrangian but I would like to know, if there is a faster or more elegant way.

Do you know of a similar problem, that has been considered before?