MATLAB: Minimisation of simultaneous complex constrained equations

complexconstrainedcurve fittingMATLABoptimisation

Hi, I'm trying to find a solver that will work for my needs. I need to fit these two functions simultaneously for a range of x's via constrained fitting parameters a and b.

S1(x)=f(x,a,b)

S2(x)=g(x,a,b)

where S1, S2, f() and g() are all complex functions of x, whereas a and b are the fitting parameters which are strictly real and constrained within positive limits. S1 and S2 are vectors containing complex experimental data, f() and g() are mathematical expressions that are unfortunately too complicated to post.

Does anyone have any ideas which solver might work for me?

Thanks

Best Answer

Split everything into real and imaginary part and use lsqcurvefit or lsqnonlin to solve for a and b.

Best wishes

Torsten.

Related Solutions

MATLAB: Constrained Polynomial Regression

So you mean that you want to constrain a cubic polynomial regression such that the x^2 term is zero?

For this I would use fsolve if you have the optimization toolbox.

If you don't, there is always the Nelder-Mead algorithm implemented as the function fminsearch.

You'd go something like this:

constraint = [1,0,1,1];  % Ignore possible x^2 term
polyFunc = @(p) polyval(p.*constraint,x);
objectiveFunc = @(p) (y - polyFunc(p)).^2;
p0 = [1, 0, 2, 3];  % It pays to have a realistic initial guess
p = fminsearch( objectiveFunc, p0 );

Instead of using polyval you could always just write the polynomial formula verbatim. However, this way you get a result that is consistent with other polynomial functions.

Warning: Nelder-Mead can be a hairy beast. Read the documentation, play around, and find ways to tame it.

MATLAB: How does one specify a real datatype when attempting to fit real parameters to a complex function with lsqcurvefit

You won't get complex values for C if you fit real(y) to real(f(x)) and imag(y) to imag(f(x)) simultaneously.

In this case, you only work with real numbers.