find minimal difference for vector (Optimalisation algorithm)

Dear Experts,

At the moment I'm trying to minimise a vector which compares experimental data with a function dependent on 3 unknown constants. Lets call these constants A, B and C. This means the function is dependent on f(x,y,A,B,C). The y-values from the experimental data must be as close as possible to the y-values of the function. Thus, I make a new vector which calculates the y-values of the function with the same x values used as for the experimental data. Now I want to compare both y-vectors and make an algorithm which uses iterations to obtain the must optimal values for A, B and C.

I know a function in matlab is present called fmincon, however this function makes use of an objective function, while I now have a vector which needs to be compared to another vector. Are there any build in matlab functions I can look into. Or is there a simple way to make this algorithm.

I would like to hear from you.

Kind regards,

Iljar Dickhof

Answer 1

[Star Strider]

In the Optimization Toolbox, one option is the lsqcurvefit function.

To use any of the others (or any of the Global Optimization Toolbox functions), it would be necessary to create a second function (here ‘fitfcn’):

x = 1:20;
y = rand(size(x));

objfcn = @(b,x) b(1) + b(2).*sin(b(3).*x);                      % Example Function, A=b(1),  B=b(2), C=b(3)
fitfcn = @(b) norm(y - objfcn(b,x));                            % Function To Fit Data
B0 = rand(3,1);                                                 % Initial Parameter Estimates
B = fmincon(fitfcn, B0)                                         % Fit Data, Return Optimised Parameters

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[Iljar Dickhof]

Is there also a way to constrain the different parameters b/B0?

[Star Strider]

Yes.

The lsqcurvefit function can use upper and lower bounds, and fmincon and some Global Optimization Toolbox functions can use additional constraints (although I rarely use any other than the bounds, and have not in several years).

EDIT — (30 Sep 2021 at 18:08)

See the fmincon documentation section beginning with Minimize with Bound Constraints and the lsqcurvefit documentation section on Best Fit with Bound Constraints for details.

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Answer 2

[Matt J]

See lsqcurvefit.

https://www.mathworks.com/help/optim/ug/lsqcurvefit.html

[Matt J]

Is there also a way to constrain the different parameters b/B0?

As you will see at the link I've provided, lsqcurvefit does let you impose upper and lower bounds.