Invalid operation: 1 / {positive convex}
The function 1/\|x\| is non-convex on \mathbb{R}^n. It remains so after adding any polynomial of \|x\|. Your P approximation may become convex on some convex subsets of \mathbb{R}^n away from 0 (your text mentions “velocity larger than”…) but it is unlikely something like that is DCP. Maybe more context would be needed.

