It is known that f(x) is convex with respect to norm(x-a)^4, am i right? So, how can i express f(x) = log(1+1/(norm(x-a)^4 ) ) in cvx?

Tell us, and show us, that it is convex. I’m disinclined to think it is.

You’ve been around long enough enough to know the forum rules on that.