find minimal difference for vector (Optimalisation algorithm)

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Iljar Dickhof 2021-9-30

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编辑： Star Strider 2021-9-30

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

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Answer 1

Star Strider 2021-9-30

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在 MATLAB Online 中打开

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 2021-9-30

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

Star Strider 2021-9-30

编辑：Star Strider 2021-9-30

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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