How can the Global minimum be got using optimization toolbox?

I have a function(sum of least squares) which I need to minimize(using fmincon).However, I get different optimized parameters for different initial values. My guess is it is finding the local minimum. Is there a way I can find the global minimum?

Answer 1

[Shashank Prasanna]

Global Optimization Toolbox offers GlobalSearch and multistart so that you can start at several starting points and hope to arrive at the global minimum.

In theory one can ever know if the minimum is global or local unless and until every point on the objective surface has been evaluated.

If you don't have the global optim toolbox, I would recommend creating several start points using rand and running fmincon in a loop or parallely using Parallel computing toolbox if you have the license to speed things up.

[Nitin Samuel]

oh...using rand and a loop seems to be a good idea for different initial points..Ill try and get back....thank you..

[yongjun wang]

Hello,I also meet the same question and I don't want to use global optimization toolbox,have you finished it,can you paste your code for reference? Thank you very much.

Answer 2

[Walter Roberson]

No, not using the Optimization Toolbox. If you use the Global Optimization Toolbox then you can automate the process of trying with different initial values, but even then the global minimum is not certain to be found.

To be sure of finding a global minimum, you need to do analysis on the function being minimized. For example if you can find bounds for the ranges where there are minima, and you can find upper bounds on the number of minima, then you have a basis to search for the global minima. Or possibly you can use calculus to help locate the minima and then search those for the global minima.

[Nitin Samuel]

oh...Is there any way where it can be done by reducing the termination tolerance to minimum possible? Or by using a code such that the iterations stop only when the coefficient of determination is closest to 1?

[Walter Roberson]

I don't think I know what "coefficient of determination" is ?

[Nitin Samuel]

oh..sorry for not elaborating..Actually I'm fitting predicted data(using iterations) with experimental data minimizing sum of least squares between the two. 'Coefficient of determination(R^2)' is the measure of how good the fit is.Closer it is to 1, better the fit. The current problem is iterations stop much before 1 because it finds a local minimum.

Matlab command- corrcoef.

So my question is, is there a way we can make the iterations stop only when it is closest to 1?

[Walter Roberson]

No there isn't, not without you analyzing the function being minimized to find bounds (etc) as I described above. Otherwise the fitting process is not going to know that any particular iteration is as good as you are going to get. And if you try to write in any fixed tolerance without doing a numeric analysis of the fitting function, then you risk the possibility of endless search.

However, if you use the Global Optimization tools Benji mentioned, you could set both a tolerance and an iteration limit, I believe. Or you can program much the same functionality yourself if you do not have that toolbox.

[Nitin Samuel]

oh..Your explanation can't get any better...Thanks a lot Mr.Roberson...