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How to figure the initial guess to optimize

  1. Dec 31, 2013 #1
    I have the following problem to code using python:

    I have 7 parameters: x,y,z,t, HF, M1F, and M2F. The user should input any of these 3 and the program should calculate the rest.

    The relations that I have are:

    HF = -xyt

    M1F = -2xzt + 4yzt - xyt + 4tz^2

    M2F = 2yzt - xyt

    1 = -2xt + 2yt + 4zt

    Attempt to solve the problem:

    I have 7 parameters and the user should input 3 => I will be left with 4 parameters. So it's all about solving a system of 4 nonlinear equations with 4 unknowns.

    I read online that scipy.optimize could be used to solve a system of nonlinear equations. But I need an initial guess.

    Going back to the physics of the problem I have the following initial conditions:

    x > 0

    y > 0

    z < 0

    HF > 0

    M1F > 0

    M2F > 0

    M2F > M1F (solving this inequality from the above equations I get: -x + y + 2z < 0)

    HF > M1F + d (solving this inequality from the above equations I get: -x + 2y + 2z < 0)

    How can these initial conditions help me get the initial guess so that I can solve my problem using scipy.optimize?
     
  2. jcsd
  3. Dec 31, 2013 #2

    mfb

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    Did you test some trivial initial guesses, like +-1?

    What is d in "HF > M1F + d"?

    As y>0, "-x + y + 2z < 0" follows from "-x + 2y + 2z < 0", so (assuming those inequalities are correct) "M2F > M1F" follows from the last inequality.
     
  4. Dec 31, 2013 #3

    AlephZero

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  5. Jan 9, 2014 #4
    I also haven't figured out the "d". I think it's a typo.
    Another constraint: t > 0
    If t is not provided, +1.0 would be as good a guess as any.
     
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