I'm using geometric programming (GP) applied to optimize an analog circuit. I must to reduce the distance to a center of a bounded box, it means a polytope defined as:
XL<=X<=XU [1]
where X is a vector x=(x1,x2,...,xn). Therefore my objective function is described by:
f(x)=min(norm(x-xc)) [2]

where xc is the center of a polytope mentioned above.

The great problem arise to define [2] as a posinomial form that supported GP. It's widely know that norm (x-xc) isn't posinomial. How can i re-define [2] such that it meet this requirement????