MathGroup Archive: January 2008 [00299]

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NMinimize Error In Evaluation
To: mathgroup at smc.vnet.net
Subject: [mg84801] NMinimize Error In Evaluation
From: "Jason S. Kong" <kongjs at gmail.com>
Date: Tue, 15 Jan 2008 03:13:49 -0500 (EST)
Hi,

I have been having an issue with NMinimize in an attempt to try to do
some optimization routines.

First, here is the background:

I want to simulate some data that was experimentally determined, and
there are a large variety of variables involved.  I do not believe
there is a simple, analytical solution to obtain my results, so I
decided to optimize it numerically, that is, NMinimize.  Below I have
some data and the method by which I attempted to solve this.  At the
end, you will see the error I get, preventing me from being able to
utilize NMinimize.  Any help on this issue would be greatly
appreciated, as this is not the first time I have had to abandon a
problem due to the same error!

At the end, I wanted to see if NMinimize had problems with functions
inside of NMinimize by writing a quick "roar" program, but it
functioned fine.

Thanks,

-Jason S. Kong

---

xvals = {6.`, 12.`, 18.`, 24.`, 36.`, 48.`, 60.`, 75.`, 90.`, 120.`,
   150.`, 180.`, 210.`, 240.`, 270.`, 300.`, 390.`, 480.`, 570.`,
   660.`, 750.`, 840.`, 912.`, 930.`, 1020.`, 1110.`, 1200.`, 1350.`,
   1524.`, 1800.`, 2442.`};

yvals = {0.03049534752960375`, 0.030612029204239437`,
   0.03088344092567462`, 0.03106269103453524`, 0.03132902963968192`,
   0.031313810290816396`, 0.03167484706668189`, 0.031816894322760116`,
    0.03173995205905108`, 0.031799138415750335`, 0.03183126815224423`,
    0.03200882722234201`, 0.03196570573388969`, 0.032041802478217314`,
    0.03191751112914886`, 0.03214072824584322`, 0.03222950778089211`,
   0.03230898660274541`, 0.03230306796707548`, 0.03227516582748868`,
   0.032589699037376185`, 0.03284927348747152`, 0.03289831361159377`,
   0.03300231249550818`, 0.03331853674415852`, 0.033540908341471456`,
   0.03361869612456192`, 0.033647443783530136`, 0.033538371783327206`,
    0.033603476775696396`, 0.03364321618662304`};

ListPlot[{xvals, yvals} // Transpose]

equilibrium[C1_, C2_, C3_, C4_, C5_] := Solve[
    {C1 == var2/(var1 var5),
     C2 == var3/var2,
     C3 == var4/var2,
     var1 + var2 + var3 + var4 == C4,
     var5 + var2 + var3 + 2 var4 == C5}, {var1, var2, var3, var4,
     var5}, WorkingPrecision -> 100] // N // Chop

imagine[tests_] :=
 Select[tests,
  And @@ {(Re[var1 /. #] == var1 /. #), (Re[var2 /. #] ==
        var2 /. #), (Re[var3 /. #] == var3 /. #), (Re[var4 /. #] ==
        var4 /. #), (Re[var5 /. #] == var5 /. #)} &]

dynamics[C1_, C2_, C3_, C4_, C5_] :=
 Select[imagine[
   equilibrium[C1, C2, C3, C4,
    C5]], #[[1, 2]] > 0 && #[[2, 2]] > 0 && #[[3, 2]] > 0 &]

data1[C1_, C2_, C3_, C4_,
  C5_] := {C5, var1} /. dynamics[C1, C2, C3, C4, C5] // Flatten
data2[C1_, C2_, C3_, C4_,
  C5_] := {C5, var2 + var3} /. dynamics[C1, C2, C3, C4, C5] //
  Flatten
data3[C1_, C2_, C3_, C4_,
  C5_] := {C5, var5} /. dynamics[C1, C2, C3, C4, C5] // Flatten

go[C1_, C2_, C3_, C4_, R1_, R2_, R3_] := (
  listdata1 = data1[C1, C2, C3, C4, #] & /@ xvals;
  listdata2 = data2[C1, C2, C3, C4, #] & /@ xvals;
  listdata3 = data3[C1, C2, C3, C4, #] & /@ xvals;
  r1 = (R1 #)/C4 & /@ (listdata1 // Transpose)[[2]];
  r2 = (R2 #)/C4 & /@ (listdata2 // Transpose)[[2]];
  r3 = (R3 #)/C4 & /@ (listdata3 // Transpose)[[2]];
  calcyvals = r1 + r2 + r3;
  error = Total[(calcyvals - yvals)^2])

NMinimize[{go[c1, c2, c3, 25, ra1, ra2, ra3],
  c1 > 0 && c2 > 0 && c3 > 0 && ra1 > 0 && ra2 > ra1 &&
   ra3 > ra2}, {c1, c2, c3, ra1, ra2, ra3}]

NMinimize::nnum: The function value (-0.0336474+0.04 var1+0.04 \
(var2+var3)+0.04 var5)^2+(-0.0336432+0.04 var1+0.04 (var2+var3)+0.04 \
var5)^2+(-<<20>>+<<2>>+0.04 \
var5)^2+(<<1>>)^2+<<1>>^2+<<1>><<1>><<1>>+(<<1>>)^2+(<<1>>)^2+(-0.\
0328493+0.04 var1+<<1>>+0.04 var5)^2+<<21>> is not a number at \
{c1,c2,c3,ra1,ra2,ra3} = {2.,2.,2.,1.,1.,1.}. >>

NMinimize[{(-0.0336474 + (ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (
     ra3 var5)/25)^2 + (-0.0336432 + (ra1 var1)/25 +
     1/25 ra2 (var2 + var3) + (ra3 var5)/25)^2 + (-0.0336187 + (
     ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (ra3 var5)/
     25)^2 + (-0.0336035 + (ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (
     ra3 var5)/25)^2 + (-0.0335409 + (ra1 var1)/25 +
     1/25 ra2 (var2 + var3) + (ra3 var5)/25)^2 + (-0.0335384 + (
     ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (ra3 var5)/
     25)^2 + (-0.0333185 + (ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (
     ra3 var5)/25)^2 + (-0.0330023 + (ra1 var1)/25 +
     1/25 ra2 (var2 + var3) + (ra3 var5)/25)^2 + (-0.0328983 + (
     ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (ra3 var5)/
     25)^2 + (-0.0328493 + (ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (
     ra3 var5)/25)^2 + (-0.0325897 + (ra1 var1)/25 +
     1/25 ra2 (var2 + var3) + (ra3 var5)/25)^2 + (-0.032309 + (
     ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (ra3 var5)/
     25)^2 + (-0.0323031 + (ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (
     ra3 var5)/25)^2 + (-0.0322752 + (ra1 var1)/25 +
     1/25 ra2 (var2 + var3) + (ra3 var5)/25)^2 + (-0.0322295 + (
     ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (ra3 var5)/
     25)^2 + (-0.0321407 + (ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (
     ra3 var5)/25)^2 + (-0.0320418 + (ra1 var1)/25 +
     1/25 ra2 (var2 + var3) + (ra3 var5)/25)^2 + (-0.0320088 + (
     ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (ra3 var5)/
     25)^2 + (-0.0319657 + (ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (
     ra3 var5)/25)^2 + (-0.0319175 + (ra1 var1)/25 +
     1/25 ra2 (var2 + var3) + (ra3 var5)/25)^2 + (-0.0318313 + (
     ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (ra3 var5)/
     25)^2 + (-0.0318169 + (ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (
     ra3 var5)/25)^2 + (-0.0317991 + (ra1 var1)/25 +
     1/25 ra2 (var2 + var3) + (ra3 var5)/25)^2 + (-0.03174 + (
     ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (ra3 var5)/
     25)^2 + (-0.0316748 + (ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (
     ra3 var5)/25)^2 + (-0.031329 + (ra1 var1)/25 +
     1/25 ra2 (var2 + var3) + (ra3 var5)/25)^2 + (-0.0313138 + (
     ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (ra3 var5)/
     25)^2 + (-0.0310627 + (ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (
     ra3 var5)/25)^2 + (-0.0308834 + (ra1 var1)/25 +
     1/25 ra2 (var2 + var3) + (ra3 var5)/25)^2 + (-0.030612 + (
     ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (ra3 var5)/
     25)^2 + (-0.0304953 + (ra1 var1)/25 + 1/25 ra2 (var2 + var3) + (
     ra3 var5)/25)^2,
  c1 > 0 && c2 > 0 && c3 > 0 && ra1 > 0 && ra2 > ra1 &&
   ra3 > ra2}, {c1, c2, c3, ra1, ra2, ra3}]

go[2., 2., 2., 25, 1., 1., 1.]

33275.9

roar[x_, y_] := x^2 + y^2
NMinimize[roar[x, y], {x, y}]

{0., {x -> 0., y -> 0.}}

-- 
Jason S. Kong
Graduate Student, Chen Lab
Department of Chemistry and Chemical Biology
Baker Laboratory, Cornell University
Ithaca, NY, 14853
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