Re: Optimizing/minimizing functions that use absolute value.

On Dec 23, 6:59 pm, David W. Cantrell <DWCantr...@xxxxxxxxxxx> wrote:
"Peter Nachtwey" <pnacht...@xxxxxxxxxxx> wrote:
"David W. Cantrell" <DWCantr...@xxxxxxxxxxx> wrote in message
news:20071223180606.540$8b@xxxxxxxxxxxxxxxxx
"Peter Nachtwey" <pnacht...@xxxxxxxxxxx> wrote:
There is then no trouble differentiating or integrating absreal.

No such luck for me.  Mathcad refuses.
Can Mathematica solve problems like this?

That depends on how simple the problem is. For example, it succeeds
with both differentiation and integration of absreal itself:

In[9]:= absreal[x_] := Sqrt[x^2]

In[10]:= D[absreal[x], x]

Out[10]= x/Sqrt[x^2]

In[11]:= Integrate[absreal[x], x]

Out[11]= (x*Sqrt[x^2])/2

(By constrast, it returns D[Abs[x], x] and Integrate[Abs[x], x]
unevaluated.)

It always succeeds with problems of the form D[absreal[f[x]], x] if it
knows how to differentiate f itself. For problems of the form
Integrate[absreal[f[x]], x], whether it succeeds depends on the
function f,
as you might suspect.

David
I finally got answers but I had to do it this way
ftp://ftp.deltacompsys.com/public/NG/Mathcad%20-%20MinITAE2.pdf

Thanks for showing that.

I still think that Mathcad is doing this using numerically instead of
symbolically.  However the answer agree pretty much with what I have be
calculating numerically.  Mathcad chokes on the symbolic solutions.   If
I do try to get an answer it runs or locks up forever.

This is a difficult problem for computer algebra systems. I have two,
Mathematica and Derive, and neither is able to do this symbolically.

At your link above, you show the results a = 1.503 and error = 1.952 .
As best I can tell (and I could be wrong!), using your a value, the error
is 1.951879 and, thus, in agreement with your error value.

But with a = 1.506, I find error = 1.951862 and so perhaps your a value was
not quite optimal. But again, I could be wrong; the numerical integration
seems difficult.

David- Hide quoted text -

- Show quoted text -
If I display 8 digits and decrease the tolerance to 0.000000001 then
a=1.50487918
ERR=1.95185944

This shows two things.
1. I don't think 3 of us can be wrong. 1.503-1.506 is closer than
1.4.
2. There must not be a way to get the exact solution symbollically.

Peter Nachtwey
.

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