11 Replies Latest reply: Feb 23, 2012 7:27 AM by dghaffaritari

# Urgent Optimization problem

I appreciate it if you could let me know if it is possible to minimize this in MathCAD. The problem is minimization of an error function with 24 constants(should be found by optimization) and 1 variable.

Error(a11,b11,d11,a12,b12,d12,a13,b13,d13,a22,b22,d22,a23,b23,d23,a33,b33,d33,a66,b66,d66,a77,b77,d77,eps)

So I want to find constant aij,bij and dij so that Error(eps) is minimum when 0<eps<0.1(at any eps), Is it possible to optimize this using Mathcad? If not would you please help me which math tool could possibly minimize this?

Thank you

Dariush

• ###### Re: Urgent Optimization problem

It's not possible to say whether or not this is possible without more information. How is the function "Error" defined? Error between what and what?

• ###### Re: Urgent Optimization problem

Richard,

The Error fucnction is symbolically defined. In the minimization part I want to find constants aij,bij,dij so that the function Error(eps) is always minimize (0<eps<0.1). Basically I don't want to find variable eps but rather have it as a variable.

Thanks

Dariush

***I also attached the file that I have here, It is in written using version 14.

Message was edited by: DanMarotta.

• ###### Re: Urgent Optimization problem

At least two of your parameters are not independent, so you have an infinte number of possible solutions. I believe that minimize has stopped at one of those solutions, which is very close to where you started. If you change the starting guesses you will find other, equally valid solutions.

Message was edited by: DanMarotta

• ###### Re: Urgent Optimization problem

Yes that is true, But you see the problem I have right now is that I am fitting parameter "eps" along with other constants, although I want to keep it as a variable. What I am really looking for is a function Error(eps) that is always minimum within the range (0<eps<0.1) . Is that possible using mathcad?

• ###### Re: Urgent Optimization problem

Yes that is true, But you see the problem I have right now is that I am fitting parameter "eps" along with other constants, although I want to keep it as a variable. What I am really looking for is a function Error(eps) that is always minimum within the range (0<eps<0.1) . Is that possible using mathcad?

Do you mean like in the attached worksheet?

Message was edited by: DanMarotta

• ###### Re: Urgent Optimization problem

Yes, In fact in the current file I uploaded, fits eps as well.

• ###### Re: Urgent Optimization problem

i think i know what you want to do，but your worksheet are too complex，you may want to find the parameters in your function through minimizing the error，the error functio can be the error(between your function and the experimental data ) sum of squares.mathcad can do it.

my work may have something in common with yours.i give you two two suggestions,hope that it can do some help for you:

1.you have two many parameters,and your functions are very complex,you can use matrix instead of so many parameters;

2.the error function can be expressed like this:

you said that "What I am really looking for is a function Error(eps) that is always minimum within the range (0<eps<0.1)",i think it depends on whether the function and the data can be fitted well or not，if they are fitted very well，the Error maybe very small.

my english is poor,maybe i misurderstand you,wo can continue to discuss.

• ###### Re: Urgent Optimization problem

键 张,

Thank you for your suggestions. I would like to re-phrase this question in this form.

Assume we have an arbitrary function like this:

F(x,c1,c2,c3):=c1.x^3+c2.log(x)+c3

now I want to find a minimum for the function F by finding c1,c2 and c3 so that for any value of the variable x (0<x<0.1) this means something like

F(x):=Minimize(F,c1,c2,c3)

Which is not possible, is it?

• ###### Re: Urgent Optimization problem

you can use the minimize function to find c1,c2 and c3

i make a simple example,you also can seek the QuickSheet for help.

• ###### Re: Urgent Optimization problem

键 张,

Thank you. I think this is going to help me solve the problem. I was trying to solve it in a contineous manner but now I think maybe decretizing, it as you did, might even make it easier to solve. I'll work on it for a few days and let you know how it goes. I appreciate your help.

Dariush

• ###### Re: Urgent Optimization problem

键 张,

What you suggested worked, Thank you again.

Dariush