How to use fminsearch for least square error minimization?

Hi everyone,

I am doing a Modal Parameter Estimation problem. I have measured values, and a function for numerical values. There is an error, which I need to minimize. But when I use fminsearch, it says that the dimensions on left hand side don't agree with that of right hand side. Becuase, fminsearch only gives 1x2, while the error (objective function) is 1x269.

I have used the following MATLAB commands:

e=@(uk) (abs(data_1(2561:2819,4))-abs((2i.*Hr.*uk(2).*uk(1).*uk(1))./(((uk(1).^2)-(ws.^2) + 2i.*uk(2).*uk(1).*ws))).^2
fminsearch(e,[413.4,0.0034])

Here, ws = 400:0.155:440

Any suggestions? Thank you for your time.

[Rik]

You need to design a function that returns a scalar. Then fminsearch will adjust the starting guesses to minimize that function.

[Muhammad Affan Arif]

@Rik So you mean, I need to design a function that minimizes the objective function at each data point?

Answer 1

[Rik]

I mean your objective function must only return 1 value, regardless of the shape of your data.

This is the standard ordinary least squares cost function. You need to provide a handle to your function, your beta will be determined by fminsearch, and you need to know the true value.

t=linspace(0,2*pi,100);
f=@(beta) sin(beta(1)*t+beta(2));
initial_guess=[1 1];
y_true=linspace(0,10,100);

OLS=@(f,beta,y_true) sum((f(beta)-y_true).^2,'all');
beta_fitted=fminsearch(@(beta) OLS(f,beta,y_true),initial_guess)

beta_fitted = 1×2

-0.0000 7.8540

Edit: sorry, I missed the squared part of the OLS.

[Muhammad Affan Arif]

Thank you, very much. It solved my issue.

I apologize for late acknowledgement.