Thread: Minimizing a nonlinear integral (in Matlab, I hope)

1. Minimizing a nonlinear integral (in Matlab, I hope)

Ok, I think this is a pretty tricky one.

I'm trying to develop a script to minimize A in the following function. It looks like I want to use the fmincon() function, but I'm not really sure. I think I just need a push in the right direction...

(int((1-(1-x)^(1/(D1)))-x*(C1),z,0,h)-P1)^2+
(int((1-(1-x)^(1/(D2)))-x*(C2),z,0,h)-P2)^2+...
=A

So there's a different value of x for every z - I need it to be able to feed it a value for z and have it return the value of x that will minimize A.

There are eight given values for each of C D and P (as in, we have C1 though C8 along with eight different terms that need to be added)

Here are some conditions which are making this extra tricky:
1) x must increase as z increases, that is dx/dz is always positive
2) x must be positive at all points
3) x must be less than 1, and preferably less than 0.5

If anybody can help me with this, you really are the best person in the universe.

Thanks!

Canopy

2. Originally Posted by canopy
Ok, I think this is a pretty tricky one.

I'm trying to develop a script to minimize A in the following function. It looks like I want to use the fmincon() function, but I'm not really sure. I think I just need a push in the right direction...

(int((1-(1-x)^(1/(D1)))-x*(C1),z,0,h)-P1)^2+
(int((1-(1-x)^(1/(D2)))-x*(C2),z,0,h)-P2)^2+...
=A

So there's a different value of x for every z - I need it to be able to feed it a value for z and have it return the value of x that will minimize A.

There are eight given values for each of C D and P (as in, we have C1 though C8 along with eight different terms that need to be added)

Here are some conditions which are making this extra tricky:
1) x must increase as z increases, that is dx/dz is always positive
2) x must be positive at all points
3) x must be less than 1, and preferably less than 0.5

If anybody can help me with this, you really are the best person in the universe.

Thanks!

Canopy
I think you should post the real/original question

CB

3. Thanks though

Ah, sadly there was no original question, so none of it was that straightforward. I'm trying to put together a model for melting of the mantle at mid ocean ridges. I think I just about have a numerical approach finished now though (one of those things where you have to ask the question in words in order to realize the answer)

But thanks for looking over it!