How to add the sign function to the atom library

Nonconvex
1

I’d like to add the sign function to the atom library but so far I haven’t been successful. Actually, I’d like to use a slightly modified version (equal to 1 when evaluated at 0) defined as

\mathop{\text{signum}}(x) = \begin{cases} 1 & \text{if } x \geq 0, \\ -1 & \text{if } x < 0. \end{cases}

Can anyone point me in the right direction for adding this function?

2

You do know this is not convex, right? Now, you can represent the signum function in certain contexts by employing binary or integer variables, but CVX’s functions are all continuous and convex/concave.