I want to use the cvx to express 1/(a^2+x^2), where a is a constant and x is a variable. It is a convex function. But I find it hard to solve it in cvx.

My code is in the following

cvx_begin

variable x

expression z

z=norm([a x]) ;

minimize ( prod_inv(z) )

subject to

x>=20;

x<=100;

cvx_end

Can you help to express 1/(a^2+x^2)? Thanks a lot.