Let me set up the problem. Assume I am operating in x \in \mathbb{R}^{2} and I have a unit disc in \mathbb{R}^{2} defined by x^{\rm T}x=1. Assume I have a bounding box \alpha_{i} \leq x_{i}< \beta_{i}. My goal is to find the point farthest from the center from the disc. So my first crack at this was

$$ {\rm min} \frac{1}{x^{\rm T}x}$$

subject to

$$x^{\rm T} x\leq 1$$

$$\alpha_{i} \leq x_{i}< \beta_{i}$$

This violated the DCP requirement. So I tried other similar cost functions like {\rm exp}(-x^{\rm T} x) and log barrier functions and I still got DCP requirement errors. Should I give up trying to massage this?