{convex} - {convex} error

Nonconvex
2

Let f(x,y) = norm(abs(x)-abs(y))

Then
f(1,-1) = f(1,1) = 0
f((1+1)/2,(-1+1)/2) = 1

f((1+1)/2,(-1+1)/2) \nleq 1/2*f(1,-1)+1/2*f(1,1)
This proves f(x,y) is not convex.