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Overwhelming problem

  1. Mar 15, 2005 #1
    This problem appeared while working on a neural networks practical.
    There are given 12 inequalities (x_0, x_1, x_2, x_3, x_4 unknown) of the form:

    [tex]x_0 + ax_1 + bx_2 + cx_3 + dx_4 >= 0[/tex]

    or,

    [tex]x_0 + ax_1 + bx_2 + cx_3 + dx_4 < 0[/tex],

    and that there exists a set of solutions that satisfy all 12 inequalities. I have to find one of those solutions but I don't know where I can start to attack this problem? I'm unable to apply trial and error, due to the high number of unknowns. I'm not finding a rigorous methodology either. Does anyone have any suggestion? Does any software package exist that aids me to do this?
    Thanks a lot!
     
    Last edited: Mar 15, 2005
  2. jcsd
  3. Mar 15, 2005 #2

    Galileo

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    I think there's an algorithm for this. Look for the Simplex method.
     
  4. Mar 15, 2005 #3

    PerennialII

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    Yeah, linear optimization/programming methods will do it for you. For example Matlab has a nice set of tools ... at least if you have access to the optimization toolbox.
     
  5. Mar 15, 2005 #4
    Maple can solve systems of linear inequalities, though its capabilities are somewhat limited. I'll give a similar problem a try later.
     
  6. Mar 15, 2005 #5
    I think that this is an optimization method.
     
  7. Mar 15, 2005 #6

    PerennialII

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    That it is ... but the idea still applies if you proceed solving as a minimization / maximization problem using the inequalities as constraint eqs ... then number of eqs wouldn't pose a problem.
     
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