I have a second-order cone constraint
$$a^2 + b^2 \leq c^2$$
where
$$ c_{\min} \leq c \leq c_{\max} $$
$$ a^2 \tan(z_{\min}) \leq b \leq a^2 \tan(z_{\max})$$
While $z_{\min} \leq 0$, $c_{\min}, c_{\max}, z_{\max} \geq 0$. This is a relaxation of an equality constraint $a^2 + b^2 = c^2$. How can I express the constraint in a form fitting disciplined convex programming (DCP) inequality requirements?
This is very much a "learning" question for me, as I'm still in the process of learning about convex optimization, DCP, and SOCP. Additional details are appreciated!