For the Lagrange Multiplier Method I have been able to find a serie of steps I must do to find the result, but I don't see quite clearly what I am supposed to do with the KKT conditions.
Lagrange Multiplier method:
- Set the constraint function equal to 0
- Create another function called the Lagrangian function by combining the objective function and the constraint
- Take the partial derivatives of the Lagrangian and set them to 0
- Solve the system of equations to get the values that minimize the objective function
KKT conditions method:
- Define the Lagrangian function
- Write the additionnal conditions
What should I do? Do I need to solve a system of equations as before ? Do I need to check that the condition hold ? What if they don't hold ?