Note that the harmonic mean is concave when all x_i are positive, but may be convex or indefinite if one or more x_i’s are negative.
In any event, see Harmonic mean in cvx . I don’t think the situation has changed subsequent to the answer provided there. Of course, use of inv_pos in effects forces the arguments to be positive, thereby achieving 1/“harmoinc mean” to be convex. I will defer to others on any further elaboration.