FindMinimum[
      2.25/Q^2 + 2.25/P^2 + 1/a + 
        2/(r^2 + R^2 + 2*R*(r^2 - a^2/4)^(1/2))^(1/2) - 9/Q - 
        3/P + (2*r^2 - R^2 - 0.9*Q^2)/P^3 + 0.9/P + 0.9/Q, {P, 2}, {Q, 
        0.6}, {R, 1.2}, {r, 1}, {a, 
        0.5}]