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Math Help - Minimizing a nonlinear integral (in Matlab, I hope)

  1. #1
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    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
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by canopy View Post
    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
    Last edited by CaptainBlack; April 29th 2009 at 12:20 AM.
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  3. #3
    Newbie
    Joined
    Oct 2008
    Posts
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    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!
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