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Re: Some linear constraints seem to be ignored in function

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  • Subject: [mg132369] Re: Some linear constraints seem to be ignored in function
  • From: Bob Hanlon <hanlonr357 at gmail.com>
  • Date: Sun, 23 Feb 2014 02:56:09 -0500 (EST)
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  • References: <20140222080533.BDB3B6A13@smc.vnet.net>

I don't know why the search methods go outside the constraints, but you can
get better results using a Method other than the default of Automatic.


$Version


"8.0 for Mac OS X x86 (64-bit) (October 5, 2011)"


Clear[ff, T, J1, J2]


ff[lxw_, lwz_, c_, d_] = -J1 (lxw + lwz) - 2 J2 c +
   T (-Log[2] - 1/2 (1 - lxw) Log[(1 - lxw)/4] -
      1/2 (1 + lxw) Log[(1 + lxw)/4] -
      1/2 (1 - lwz) Log[(1 - lwz)/4] -
      1/2 (1 + lwz) Log[(1 + lwz)/4] +
      1/2 (1 - d) Log[(1 - d)/16] +
      1/8 (1 + 2 c + d - 2 lwz - 2 lxw)*
       Log[1/16 (1 + 2 c + d - 2 lwz - 2 lxw)]);


cons = And @@ Cases[ff[lxw, lwz, c, d],

  Log[x_] -> x > 0, Infinity] // Simplify


d < 1 && lwz < 1 && 1 + lwz > 0 && 1 + 2 c + d > 2 (lwz + lxw) && lxw < 1
&&
 1 + lxw > 0


T = 10;
J1 = 1;
J2 = -2/10;


Off[NMinimize::nrnum]


NMinimize[{ff[lxw, lwz, c, d], cons}, {lxw, lwz, c, d}]


{-4.91624, {c -> 0.94525, d -> -0.315535, lwz -> 0.901231, lxw ->
-0.191668}}


NMinimize[{ff[lxw, lwz, c, d], cons}, {lxw, lwz, c, d},
 Method -> "DifferentialEvolution"]


{-12.5767, {c -> -0.236399, d -> -0.976973, lwz -> -0.68191,
  lxw -> -0.939971}}



Bob Hanlon




On Sat, Feb 22, 2014 at 3:05 AM, Daniel Stariolo
<daniel.stariolo at gmail.com>wrote:

> I'm trying to minimize a non-linear function of four variables with some
> linear constraints. Mathematica 8 is unable to find a good solution giving
> complex values of the function at some point in the iteration. This implies
> that one or some contraints are not being enabled in the process. Is this a
> bug or limitation of the optimization function ?
>
> Function to minimize is
>
> ff[lxw_, lwz_, c_, d_] := - J1 (lxw + lwz) - 2 J2 c +
>   T (-Log[2] - 1/2 (1 - lxw) Log[(1 - lxw)/4] -
>      1/2 (1 + lxw) Log[(1 + lxw)/4] -
>      1/2 (1 - lwz) Log[(1 - lwz)/4] -
>      1/2 (1 + lwz) Log[(1 + lwz)/4] + 1/2 (1 - d) Log[(1 - d)/16] +
>      1/8 (1 + 2 c + d - 2 lwz - 2 lxw) Log[
>        1/16 (1 + 2 c + d - 2 lwz - 2 lxw)])
>
> where
>
> T = 10;
> J1 = 1;
> J2 = -0.2;
>
> are constant parameters. Then I try
>
> NMinimize[{ff[lxw, lwz, c, d],
>   2 c + d - 2 lwz - 2 lxw  >= -0.999 && -0.999 <= lxw <=
>    0.999 && -0.999 <= lwz <= 0.999 && -0.999 <= c <= 0.999 &&
>   d <= 0.9999}, {lxw, lwz, c, d}]
>
> with the result
>
> NMinimize::nrnum: "The function value 5.87777-4.87764 I is not a real
> number at {c,d,lwz,lxw} = {-0.718817,-1.28595,0.69171,-0.932461}."
>
> I would appreciate if someone can give a hint at what is happening here.
>
>




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