For the second one, How to reformulate this in a CVX way: Cube over Square - #31 by Mark_L_Stone , but you’ll need to restrict a > 0,which the geo_meanformulation automatically does, because the expression is concave fora < 0`;
For the first one, add an extra a as an argument of geo_mean in the above link. Similarly, you’ll need to restrict a > 0, which the geo_mean` formulation automatically does.
The provided link ultimately points back to @Erling 's formulation.