# Lagrange multipliers split Lagrangians

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.

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Interesting, if you have an alaytic $f$, it would help if you could paste it here. I don't think it is any more complex to handle another boundry constraint...
Maybe the problem is an anemic solver... can you try representing the problem differently? Let $f$ be your optimization function, then you can explicitly constrain $0 < f < 1$ (instead of using a complex expression which a dumb solver may not identify with the optimization function) and then minimize $f$.
I.e. if you are minimizing some complex expression, constrain $f=\{\text{that expression}\}$ and add a constraint $0 < f < 1$ and then minimize $f$...
@user86377 I don't understand - are you minimizing $$\sum_{k=1}^N \left( f \left(x,y,\vec{v}_k \right) - y_k \right)^2$$ for some fixed $\vec{v}_k, y_k, f$ over parameters $x,y$ and want to constrain that $f\left(x,y,\vec{v}_k \right) \in (0,1) \forall x,y,\vec{v}_k$? – gt6989b Jul 17 '13 at 15:47
I want to fit a curve.Let d, be the points of that curve.So I want to minimize the nonlinear error $$\sum_{k=1}^N \left( f \left(x,y \right) - d_k\right)^2$$ s.t $$g\left(x,y \right) \in (0,1)$$ with the optimal combination of (x,y) – user86377 Jul 18 '13 at 8:26
@user86377 You mean $f(x,y) \in (0,1)$ or $g$ is realy indended to be a different function? – gt6989b Jul 18 '13 at 13:04