FindMinimum[
      2.25*1.0289716/P^2 + 2.25*1.23924503/Q^2 + 1/(P + Q + R) - 9/P - 
        2/(P + Q) - 3/Q + R^2/Q^3 + 3*0.29125954/Q + 3*0.27885572/P, {P, 
        0.6}, {Q, 2.0}, {R, 0.5}]

FindMinimum[
      2.25*1.02480344/P^2 + 2.25*1.23244364/Q^2 + 1/(P + Q + R) - 9/P - 
        2/(P + Q) - 3/Q + R^2/Q^3 + 3*0.28887416/Q + 3*0.27877144/P, {P, 
        0.5}, {Q, 3.0}, {R, 
        0.5},  {AccuracyGoal  ->   16},  {WorkingPrecision  ->  14}]