topic Re: Minimize: 6 variables and 4 equations in Mathcad

Minimize: 6 variables and 4 equations

ValeryOchkov — Thu, 18 Apr 2019 06:24:25 GMT

One mathematician has said me that if you have 6 parameters in the minimize function - you must have 6 or more equations in this solve block. I have only 4! Is it correct?

See please one interesting problem in attach!

Thanks!

Re: Minimize: 6 variables and 4 equations

Werner_E — Thu, 18 Apr 2019 08:53:54 GMT

The less equations (or the more variables) the more solutions, resp. the more degrees of freedom.

So its easier for the solver to find a solution but this solution will heavily depend an the choice of the guess values.

As you can see below you can check the quality of the solution by evaluating the built-in variable ERR (its exactly this variable which Mathcad tries to minimize) and you may consider adding some additional constraints like aL>0 or the like, to avoid unwanted solutions.

Re: Minimize: 6 variables and 4 equations

ValeryOchkov — Thu, 18 Apr 2019 13:11:49 GMT

Thanks, Werner!

I think (guess) it (degrees of freedom) is more for the Find not for Minimize/Maximize Function.

See please the problem with 9 variables and 5 equations

Re: Minimize: 6 variables and 4 equations

Werner_E — Thu, 18 Apr 2019 15:07:39 GMT

@ValeryOchkov wrote:

Thanks, Werner!

I think (guess) it (degrees of freedom) is more for the Find not for Minimize/Maximize Function.

It applies in a similar way to a solve block with "minimize", too.

The less constraints and the more variables to change, the more possibilities to find different but equally good solutions. Ever so often in such cases depending on the equations given Mathcad possibly won't even change the guess value of the one or other variable given.

In your new sheet its quite interesting that we get the very same results using "find" and without referencing PE in any way!?

Re: Minimize: 6 variables and 4 equations

ValeryOchkov — Thu, 18 Apr 2019 16:49:10 GMT

Yes!

Now I see - we need n variables and >=n equations!

Re: Minimize: 6 variables and 4 equations

ValeryOchkov — Fri, 19 Apr 2019 05:40:04 GMT

@ValeryOchkov wrote:

Yes!

Now I see - we need n variables and >=n equations!

We have different guess values nd get different answers