How to get an additional output from fminsearch

I have been trying to implement a nested fminsearch, but I have difficulty to pass the result of the inner fminsearch to the main file. Here is a structure of my code

%%%% main.m file
fun1Ch2 = @(coeff1)outerfunc(coeff,input-parameters);
[coeff,Chi2] = fminsearch(fun1Ch2, guess);


%%%% outerfunc.m file
function [chi2,coeff] = outerfunc(coeff,input-parameters)

%=== some calculations here ====

fun2Ch2 = @(coeff2)innerfunc(coeff2,input-parameters);
[coeff2,Chi2] = fminsearch(fun2Ch2, guess);

Now the question is that how to pass the parameter coeff2 which is the result of the inner fminsearch to the main file.

Thanks in advance!

[Torsten]

function [chi2,coeff] = outerfunc(coeff,input-parameters)

I wonder why your function has two output arguments. Which one do you want to pass to your outer "fminsearch" - chi2 or coeff ? And where do you compute them in "outerfunc" ? I only see Chi2 and coeff2.

To get coeff2, define it as an output argument of "outerfunc" and call "outerfunc" with the solution of the outer "fminsearch".

[Erich]

I have two arguments because I also want to get the value which corresponds to fval. Let's say I want to pass both. There should not be any limitation. Of course, there is another file names as innerfunc.m.

"To get coeff2, define it as an output argument of "outerfunc" and call "outerfunc" with the solution of the outer "fminsearch"."

This does not work in my example.

Answer 1

[Walter Roberson]

Which one?

The last function call made by fminsearch() is typically not one that made the final improvement. If it had made an improvement, fminsearch() would generally have continued searching. I say "generally" because there is the situation where fminsearch() will stop if it determines there has not been enough improvement to bother continuing -- but a fair portion of the time fminsearch() stops when it determines that all if its attempts to improve have been useless, that some earlier call gave back the best result.

[Erich]

Thanks for your answer, Walter!

However, I seems that my simplified explanation isn't good enough. The outer and inner fminsearch functions are minimizing different parameters, so it is not for the purpose of improvement. It is like minimizing the following function

f(a,b,A,Z) = a * ( b * A - Z)

and the outer fminsearch finds the best a and inner fminsearch finds the best b. The reason why both are not optimized in a single fminsearch is because different approaches are used to optimized a and b.

[Walter Roberson]

Let's say the outer fminsearch() calls fun1Ch2 (say) 10 times, and (for illustration) say the 7th call was the one with minimum value, with the remaining 3 calls used to probe in other directions and discover that they do not improve the situation. Now, at the time that fun1Ch2 is being called the 7th time (in this scenario) it cannot know that it is going to be the call that gives the best result, so it would not be appropriate for it to save anything to "one true output".

What can you do? Well, you could have outerfunc store the most recent coeff2 value in some "accessible" location. And you program an OutputFcn https://www.mathworks.com/help/matlab/math/output-functions.html for the outer fminsearch, which will code to examine the current outerfunc result and determine whether it is the best so far, and if so retrieve the current saved coeff2 value and save it elsewhere. And then after the outer fminsearch is finished, pull out the stashed coeff2 value that the outputfcn saved.

The situation would be a bit more complicated if you were doing fmincon() instead of fminsearch(). fminsearch() is considered an unconstrained search, but fmincon() would run into the possibility that the "best" return value from outerfunc might turn out to be in an area blocked by constraints, so the outputfcn would have to check constraints as well to determine whether to save the value.

[Erich]

The solution you suggested for getting the best fit is what I have been doing already. I repeat the fit using different initial guesses and store all the coeff and chi2 in an array, and at the end I use the best value from the stores information. To do so, I have to have information from the inner fminsearch() along with the results from the outer fminsearch(). So the problem is that the only solution that I can think of is to write/read "coeff2 and Chi2" in/from a file which is quite primitive solution to me.

Regarding your suggestion "OutputFcn" was one of the first thing I tried already, but seems not working well in problem described here.

[Walter Roberson]

I have used the outputfcn of fminsearch to apply constraints, by stashing away the current result if the constraint is not violated, and by triggering termination if the constraint was violated. So I know for certain that it is possible to use the technique of having fminsearch outputfcn store current value in some accessible location for retrieval afterwards.

[Erich]

To be more exact;

inside the outerfunc function I do this

if(min(coeff_A(:,end))>Chi2_outer)

dlmwrite(file_name, [coeff_outer coeff_inner Chi2_outer],'-append', 'delimiter',',', 'precision','%10.10f');

end

which means that I store all valuable information to be used at the end. Maybe I couldn't make OutputFcn work.