How to add constraints to an existing optimization function?

I have measured y values ( y_meas) at different x values ( x1,x2 ). The relationship between x1,x2 and y_meas is described with a physical law. The law needs 4 additional parameters (vParam).

Physical Law: vParam(1)*sinh(vParam(4)*x2)^vParam(3)*exp(-vParam(2)/(x1*R))

I set up a function to find the these parameters.

 function y=fct(vParam,x1,x2,y_meas)
    % Parameters, x values, y result values
    R=8.314;
    y=0;
    for i=1:length(x1)
        y=y+(y_meas(i)-(vParam(1)*sinh(vParam(4).*x2(i)).^vParam(3).*exp(-vParam(2).*x1(i).^-1*R^-1))).^2;
    end

By now, this optimization works. But the result depends strongly on the initial values of vParam which leads to non-physical solutions. As a consequence, I want to define constraints for vParam. Unfortunately I have no idea how to do that.

Can anyone help me? Thanks in advance!

[Torsten]

What solver do you use at the moment ?

What kind of constraints do you want to define ?

In lsqcurvefit, you can introduce bound constraints on the parameters.

In fmincon, you can introduce more general constraints.

Best wishes

Torsten.

[el_nino]

lsqcurvefit helped. Thanks a lot!