inv_pos(A)+inv_pos(B) (moderator note: the expression in the title is convex, but the problem in the question is not)

If A and B are both variables, that inequality is not convex, because
1/(A*B) - 0.5*(1/A+1/B)^2 is concave in A and `B, and the other terms in the inequality are affine.

if the direction in the inequality were reversed, the constraint would be convex.