Some linear constraints seem to be ignored in function NMinimize with
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- Subject: [mg132366] Some linear constraints seem to be ignored in function NMinimize with
- From: Daniel Stariolo <daniel.stariolo at gmail.com>
- Date: Sat, 22 Feb 2014 03:05:33 -0500 (EST)
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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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