# Express 1/(a^2+x^2) in cvx

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.

Sorry, there is an obvious mistake in the code I wirte. Please ignore it. But I still want to express 1/(a^2+x^2) in cvx.

This function is only convex on a sub-interval of its natural domain. Such things are notoriously hard to model using DCP rules.

1 Like

Indeed, it is only convex for x^2 \ge a^2/3 (which, although only mattering as a piece of trivia, is itself a non-convex region).

I guess this is another expression for @Erling’s challenge., which, as shown below, does not exclude expressions which are not convex over their entire natural domain. Maybe the challenge should be clarified to include that provision.

Conic modeling challenge by https://twitter.com/e_d_andersen Do you have a nonlinear constraint that can be written in a modeling language, but can’t be represented with linear, socp, sdp, exponential cone and power cones?