# Problems with fminsearch giving startvalues as result

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Marc Laub on 25 Apr 2022
Edited: Matt J on 28 Apr 2022
Hey,
I am trying to minimize Gibbs enthalpie dependant an phase fraction and phase compositions. So i set up an equation which has all dependencys in it and is dependent on 2 variables.
The problem is that fminsearch is doing nothing, it always gives ma my start values back as results. From the outout I can see that it did 39 iterations ans tells me that the result lie within the TolX and Tolfun, but thats not the case. With a simple parameter sweep I get better results than fminsearch.. I also changes Tolx and Tol fun to very small values but that didnt help either. No matter how stupid my starting values are, thats its result, no matter how bad it is.
I also had this phenomen when doing fits with custom functions, sometimes als here that start values were given back as fit parameters without any improvement.
Does anybody know what I am doing wrong?
Best regards.
Walter Roberson on 26 Apr 2022
Are you truly working with polynomials? Or are you working with multinomials? Do you have any terms which end up using variable_1 * variable_2, or could it be separated out into the sum of two polynomials each in a single variable?

Torsten on 25 Apr 2022
Edited: Torsten on 25 Apr 2022
polynom_1 = @(variable_1,variable2) polynom(variable_1,variable2,input_1,input_2,..,input_n);
polynom_2 = @(variable_1,variable2) different_polynom(variable_1,variable2,input_1,input_2,..,input_n);
fun = @(variable_1,variable2) polynom_1(variable_1,variable_2)-polynom_2(variable_1,variable_2);
fun = @(x)fun(x(1),x(2));
x0 = [startvalue_1, startvalue2];
x = fminsearch(fun,x0,options)
Marc Laub on 26 Apr 2022
Unfortunately it did not get the correct answer. Difference from its found f(x,y) solution to the known value was more than 10^5, whereas the start value has only a difference of 90.

Matt J on 26 Apr 2022
Edited: Matt J on 27 Apr 2022
With a simple parameter sweep I get better results than fminsearch.
I don't know how you've implemented the sweep, but I don't see why you don't use that as your solution, or at least use it to initialize fminsearch. Since you know a local region where the minimum is located, I picture the sweep done in a vectorized fashion like below. It should be easy to vectorize the operation in fun() if they are just polynomial operations.
[var1,var2]=ndgrid(linspace(__), linspace(___))
Fgrid=fun(var1,var2) ; %vectorize fun() to accept array-valued input.
[~,iopt]=min(Fgrid(:));
var1_optimal=var1(iopt);
var2_optimal=var2(iopt);
Matt J on 28 Apr 2022
Just make the change of variables var1-->var1^2, var2-->var2^2 to ensure they only present positive values to the objective function. That's what fminsearchbnd does anyway.

R2020b

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