An issue about MultiStart with lsqcurvefit

Hello there.

Im working on fitting my function to experimental data using lsqcurvefit and MultiStart in order to find out the global minimum values.

And I found out that x0, lb, ub and NumStartPoints affected to x values.

So here are my questions :

1. When I set ub 1e8 to 1e10, x values became 1e7 order to 1e9 order approximately. Why this phenomena occurred? And how do I set the feasible lb and ub?

2. I compared x values between using lsqcurvefit and lsqcurvefit+MultiStart. And I found out that order of x values are higher and near ub in case of lsqcurvefit+MultiStart. Could you explain how this result occurred?

3. Final question. When I control and set those conditions ( x0, lb, ub and NumStartPoints), x values were calculated in different values every times. As I working on my problems, how do I determined the feasible results?

    myfun = @(x,xdata)(x(1).*x(2)*0.97.*x(4).*(xdata-2.2e-10)./(1+(x(2)*0.97).^0.5+x(3)*0.03+x(4).*xdata).^3)

xdata = [4.84037e-10;1.20314e-09;1.38743e-09;1.75941e-09;3.11749e-09;2.18567e-09;2.22319e-09;6.30723e-09;9.09648e-09;2.5766e-08;1.53398e-08;1.4891e-08;1.40325e-08;1.15354e-08;2.21674e-08;2.59195e-08] ; %16*1 double%
ydata = [0.1;0.2;0.3;0.4;0.5;0.6;0.7;0.8;0.9;1;1.1;1.2;1.3;1.4;1.5;1.6]; %16*1 double%
x0 = [10, 10, 10, 10] or [100, 100, 100, 100] or [1000, 1000, 1000, 1000] or [1e4, 1e4, 1e4, 1e4]
lb = [1e-8 1e-8 1e-8 1e-8];
ub = [1e8 1e8 1e8 1e8];
problem = createOptimProblem('lsqcurvefit','x0',x0,'objective',myfun,'lb',lb,'ub',ub,'xdata',xdata,'ydata',ydata);
ms = MultiStart('PlotFcns', @gsplotbestf);
[xmulti, errormulti] = run(ms, problem, 500) %NunStartPoints were set as 50, 500, 500 or rs=RandomStartPointSet('NumStartPoints',1000)%

Thank you for checking my questions.

[Torsten]

The questions can not be answered without knowledge of your data and your fit function.

Best wishes

Torsten.

[HYOJAE LEE]

I just update my data and fit function and some codes I using.

It will be helpful if you check and comment about these codes and functions.

Thanks

Lee.

[Torsten]

Choosing 4 parameters for fitting in your case makes the problem underdetermined.

As function, use

(xdata-2.2e-10)/(x(1)+x(2)*xdata)^3

with

x(1) >= 1 and x(2) >= 1e-8.

Best wishes

Torsten.

[HYOJAE LEE]

Torsten

Thank you for your advice.

I just tried what you told but x(1) and x(2) couldnt determined because errormulti(Best Funtions Values) were about 15 and x values didnt change from x0.

In this time, x0 = [100, 100]

And I got same results using function as

x(3).*(xdata-2.2e-10)/(x(1)+x(2)*xdata)^3

fitting results were

[xmulti,errormulti] = run(ms,problem,5000)

MultiStart completed the runs from all start points.

All 5000 local solver runs converged with a positive local solver exit flag.

xmulti =

     100   100

errormulti =

     14.9600

What am I missing?

[Torsten]

You can also work with the function

    x(1)*(xdata-2.2e-10)/(1+x(2)*xdata)^3

Because your y-data are in the range 0.1 - 1.6, a starting guess with x(1)=1e8 and x(2)=0 might work.

Best wishes

Torsten.