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How to resolve "function value X is not a number" issue?

Peter Bergmann
Posted 9 years ago

Dear Community,

I am just new to Mathematica that came with my Raspberry Pi2. For a while now I have been looking for a program, which is able to minimize a discontinuous and nonlinear problem. Up to now I created the following formulas:

f1[x_] := 
 Piecewise[{{0.00000000000252413096488599 x^4 - 
     0.0000000295981935774312 x^3 + 0.0001268180409138660 x^2 - 
     0.239339875030011 x + 368.934089585833, x > 0}, {0, x <= 0}}]

f2[x_] := 
 Piecewise[{{0.00000000000327848026710691 x^4 - 
     0.0000000379764365996404 x^3 + 0.0001584280843487410 x^2 - 
     0.284905693712486 x + 386.639837124850, x > 0}, {0, x <= 0}}]

f3[x_] := 
 Piecewise[{{0.00000000000273770414832564 x^4 - 
     0.0000000245466477791088 x^3 + 0.0000876247218487314 x^2 - 
     0.151272246878742 x + 298.178569447775, x > 0}, {0, x <= 0}}]

f4[x_] := 
 Piecewise[{{0.00000000000151824463118546 x^4 - 
     0.0000000164748347339070 x^3 + 0.0000716029554621768 x^2 - 
     0.140270401260495 x + 293.998348739492, x > 0}, {0, x <= 0}}]

NMinimize[{f1[w] + f2[x] + f3[y] + f4[z], 
  Plus[w, x, y, z] == 7000}, {w \[Element] Interval[{0, 4000}], 
  x \[Element] Interval[{0, 4000}], y \[Element] Interval[{0, 3000}], 
  z \[Element] Interval[{0, 3000}]}]

Unfortunately now I get the following error messages three times before the calculation is aborted:

During evaluation of In[8]:= NMinimize::nnum: The function value {812.066} is not a number at {Subscript[w, 1],Subscript[x, 1],Subscript[y, 1],Subscript[z, 1]} = {1052.02,1848.71,2479.67,1619.59}.

Is there any quick way of resolving this issue? Did I enter something in a wrong way? At least the sum of the resulting values for w,x,y, and z being 7000 is correct, maybe 812,066 is a local minimum already. But why is there an error message? I also tried to use Minimize and different Methods, but the outcome is the same in all cases.

And it is just a LOCAL minimum: As one might be able to see from the equation, fx[0]=0. A minimum value, f.e. for the entered w+x+y+z==7000, should incorporate that some of the functions are set to zero! Is there any way to include this possibility in a fast way? Or do I have to write a minimization for all 16 possibilities and minimize these again?

Best regards, Peter
POSTED BY: Peter Bergmann
6 Replies
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Peter Bergmann
Peter Bergmann
Posted 9 years ago

I edited the problem and get pretty good results with:

f[reqpower_] := MininmalBy[{
  Check[NMinimize[{ae1[w], {w == reqpower, 0 <= w <= maxae1}}, {w}, 
    Method -> "RandomSearch"], 999999],
  Check[NMinimize[{ae2[x], {x == reqpower, 0 <= x <= maxae2}}, {x}, 
    Method -> "RandomSearch"], 999999],
  Check[NMinimize[{ae3[y], {y == reqpower, 0 <= y <= maxae3}}, {y}, 
    Method -> "RandomSearch"], 999999],
  Check[NMinimize[{ae4[z], {z == reqpower, 0 <= z <= maxae4}}, {z}, 
    Method -> "RandomSearch"], 999999],
  Check[NMinimize[{ae1[w] + ae2[x], {w + x == reqpower, 
      0 <= w <= maxae1, 0 <= x <= maxae2}}, {w, x}, 
    Method -> "RandomSearch"], 999999],
  Check[NMinimize[{ae1[w] + ae3[y], {w + y == reqpower, 
      0 <= w <= maxae1, 0 <= y <= maxae3}}, {w, y}, 
    Method -> "RandomSearch"], 999999],
  Check[NMinimize[{ae1[w] + ae4[z], {w + z == reqpower, 
      0 <= w <= maxae1, 0 <= z <= maxae4}}, {w, z}, 
    Method -> "RandomSearch"], 999999],
  Check[NMinimize[{ae2[x] + ae3[y], {x + y == reqpower, 
      0 <= x <= maxae2, 0 <= y <= maxae3}}, {x, y}, 
    Method -> "RandomSearch"], 999999],
  Check[NMinimize[{ae2[x] + ae4[z], {x + z == reqpower, 
      0 <= x <= maxae2, 0 <= z <= maxae4}}, {x, z}, 
    Method -> "RandomSearch"], 999999],
  Check[NMinimize[{ae3[y] + ae4[z], {y + z == reqpower, 
      0 <= y <= maxae3, 0 <= z <= maxae4}}, {y, z}, 
    Method -> "RandomSearch"], 999999],
  Check[NMinimize[{ae1[w] + ae2[x] + ae3[y], {w + x + y == reqpower, 
      0 <= w <= maxae1, 0 <= x <= maxae2, 0 <= y <= maxae3}}, {w, x, 
     y}, Method -> "RandomSearch"], 999999],
  Check[NMinimize[{ae1[w] + ae2[x] + ae4[z], {w + x + z == reqpower, 
      0 <= w <= maxae1, 0 <= x <= maxae2, 0 <= z <= maxae4}}, {w, x, 
     z}, Method -> "RandomSearch"], 999999],
  Check[NMinimize[{ae1[w] + ae3[y] + ae4[z], {w + y + z == reqpower, 
      0 <= w <= maxae1, 0 <= y <= maxae3, 0 <= z <= maxae4}}, {w, y, 
     z}, Method -> "RandomSearch"], 999999],
  Check[NMinimize[{ae2[x] + ae3[y] + ae4[z], {x + y + z == reqpower, 
      0 <= x <= maxae2, 0 <= y <= maxae3, 0 <= z <= maxae4}}, {x, y, 
     z}, Method -> "RandomSearch"], 999999],
  Check[NMinimize[{ae1[w] + ae2[x] + ae3[y] + 
      ae4[z], {w + x + y + z == reqpower, 0 <= w <= maxae1, 
      0 <= x <= maxae2, 0 <= y <= maxae3, 0 <= z <= maxae4}}, {w, x, 
     y, z}, Method -> "RandomSearch"], too much power needed]},
  First]

When evaluating this formula with f[reqpower], the result looks like this:

MininmalBy[{999999, 999999, 999999, 999999, {396.497, {w -> 3160.39, 
   x -> 1839.61}}, {390.376, {w -> 2515.03, 
   y -> 2484.97}}, {389.794, {w -> 3140.25, 
   z -> 1859.75}}, {389.996, {x -> 2293.23, 
   y -> 2706.77}}, {389.955, {x -> 3241.48, 
   z -> 1758.52}}, {383.048, {y -> 2730.85, 
   z -> 2269.15}}, {602.931, {w -> 1733.48, x -> 1638.86, 
   y -> 1627.66}}, {600.422, {w -> 1755.15, x -> 1655.01, 
   z -> 1589.84}}, {596.013, {w -> 1752.93, y -> 1659.67, 
   z -> 1587.4}}, {592.798, {x -> 1674.27, y -> 1707.44, 
   z -> 1618.29}}, {602.931, {w -> 1733.48, x -> 1638.86, 
   y -> 1627.66, z -> 0.}}}, First]

Is there a trick to get the final result without having to look for the minimum list of values manually? According to the help database, MinimalBy[Arg,First] should do it...? Thanks a lot to whoever supports me on this! :)

EDIT: Corrected brackets, but no change in the outcome...
POSTED BY: Peter Bergmann
Peter Bergmann
Peter Bergmann
Posted 9 years ago

Okay, I found the mistake... It was a typo (MininmalBy instead of MinimalBy), sorry for bothering. -.-
POSTED BY: Peter Bergmann
Peter Bergmann
Peter Bergmann
Posted 9 years ago

This is great, Bill, thanks a lot! Is there any Explanation for this behavior? Just want to be able to avoid this in the future...
POSTED BY: Peter Bergmann
Bill Simpson
Bill Simpson
Posted 9 years ago
POSTED BY: Bill Simpson
Peter Bergmann
Peter Bergmann
Posted 9 years ago

Hi Bill, thanks for this very visual explanation! But the meaning of the RandomSearch Method was relatively clear for me. I should have staded my question more precisely, because I referred to writing the constraints with 0<=x<=4000 instead of using intervals or something like x,y,z >=0 and x,y<=3000, which I had before and also resulted in the same error message...?
POSTED BY: Peter Bergmann
Bill Simpson
Bill Simpson
Posted 9 years ago

This works without error

In[6]:= NMinimize[{f1[w] + f2[x] + f3[y] + f4[z], {w + x + y + z == 7000,
   0 <= w <= 4000, 0 <= x <= 4000, 0 <= y <= 3000, 0 <= z <= 3000}}, {w, x, y, z}]

Out[6]= {793.412, {w -> 1829.54, x -> 1709.12, y -> 1791.87, z -> 1669.47}}

For this problem this happens to find a smaller minimum

In[7]:= NMinimize[{f1[w] + f2[x] + f3[y] + f4[z], {w + x + y + z == 7000,
   0 <= w <= 4000, 0 <= x <= 4000, 0 <= y <= 3000, 0 <= z <= 3000}}, {w, x, y, z}, 
   Method -> "RandomSearch"]

Out[7]= {583.291, {w -> 2153.49, x -> 0., y -> 2663.08, z -> 2183.44}}

And this finds an even smaller minimum.

In[8]:= NMinimize[{f1[w] + f2[x] + f3[y], {w + x + y == 7000, 
   0 <= w <= 4000, 0 <= x <= 4000, 0 <= y <= 3000}}, {w, x, y}, 
 Method -> "RandomSearch", MaxIterations -> 10^4]

Out[8]= {384.535, {w -> 4000., x -> 0., y -> 3000.}}

I suspect almost any minimization method is going to have problems where some or all your functions have smoothly growing very large values adjacent to isolated points where the functions are much smaller. So if you have functions like that then I suspect that your idea of checking all the isolated points, in addition to using a general minimization method, might be the best approach.
POSTED BY: Bill Simpson
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