i have a non linear optimization problem and i am trying to solve it via lagrange multipliers.
I have 2 constraints, one with a lower bound that requires $f>0$ and one with an upper bound that requires $f<1$. The problem is very complicated so i solve it in 2 steps, using 2 different lagrangians, one for each constraint. So i search for a combination from the results that satisfies my constraints.
In some cases, because i have vectors as inputs, i did not manage to to get a solution $(x,y)$ that satisfies both $f>0$ and $f<1$. Is it because i split the problem? Thanks in advance
P.S i tried not to split the problem, and have one lagrangian with 2 constraints but because of the complexity of maths, maple and matlab did not return values. Thanks in advance.