Unconstrained Optimization with Additional Parameters

Hello

I have a problem which is very similar to this unconstrained optimization example using fminunc with additional parameters here (bowlpeakfun function example):

http://www.mathworks.com/products/optimization/demos.html?file=/products/demos/shipping/optim/tutdemo.html

My problem is that I want to use the large Scale algorithm where the derivatives of the objective function are supplied. Therefore if I rewrite my objective function as

function [y, grad] = bowlpeakfun(x, a, b, c)
y = (x(1)-a).*exp(-((x(1)-a).^2+(x(2)-b).^2))+((x(1)-a).^2+(x(2)-b).^2)/c;
if nargout >1 
   grad = gradient of y;
end

And then set the anonymous function/optimization as

a = 2;b = 3; c = 10;
f = @(x)bowlpeakfun(x,a,b,c)
x0 = [-.5; 0];
options = optimset('GradObj','on');
[x, fval] = fminunc(f,x0,options)

I get an error 'Failure in initial user-supplied objective function evaluation. FMINUNC cannot continue' which I think its related somehow to the fact that the anonymous function doesn't see that there is a gradient associated with bowlpeakfun. Redifining the anonymous function as

[f,grad] = @(x)bowlpeakfun(x,a,b,c)

does not work either. Any help much appreciated.

Thanks

Answer 1

[Alan Weiss]

I assume that your line

   grad = gradient of y;

is not intended to be taken literally, but you are just saving the space that would be taken by writing the entire gradient.

Have you tried to evaluate

[fval gradfval] = f(x0)

to see why MATLAB is throwing an error?

Answer 2

[Javer]

Hi Alan

Thanks for the help. Yes,

grad = gradient of y;

is not to be taken literally. It is just the gradient of the function. To clarify, my function is

function [y, grady] = myfun(x, params)
   y = f(x,params)        % x is the variable, params are the parameters
if nargout >1 
   grady = f'(x,params);  % f' gradient of y wrt x
end

If I set fminunc to use the Medium Scale algoritm and then set the anonymous function/optimization as

params = 'given values'
f = @(x) myfun(x,params)
x0 = ['any initial values'];
options = optimset('LargeScale','off');  
[xnew, fval] = fminunc(f,x0,options)

There is no problem and I get my solution; the optimiser will work out the derivatives numerically. Now, what I want is to be able to use my own analytical derivatives with the Large-Scale algorithm. So, if I write

params = 'given values'
[f gradf] = @(x) myfun(x,params)

Matlab doesn't like this anonymous function and throws 'Error: Only functions can return multiple values'. If I now set the problem as (hoping Matlab will pick out my supplied analytical derivatives)

params = 'given values'
f = @(x) myfun(x,params)
x0 = ['any initial values'];
options = optimset('GradObj','on');
[xnew, fval] = fminunc(f,x0,options)

Matlab will throw another error

??? Error using ==> uminus Too many output arguments.... Caused by: Failure in initial user-supplied objective function evaluation. FMINUNC cannot continue.

So, it seems what I am having problems with is setting up the problem correctly.

Thanks

[Walter Roberson]

grady = f'(x,params);

is not a valid line of code. The "'" character cannot occur in that syntax.

[Javer]

Sorry, with the ' in f'(x,params) I only meant that myfun returns both the function value and the derivative if requested, whichever they might be.

Answer 3

[Walter Roberson]

Use a subfunction instead of an anonymous function to pass the additional parameter, and pass the handle to the subfunction to fminunc .

Answer 4

[Javer]

Thanks Walter

It seems I am not being lucky with that approach either. My function is as created above:

function [y, grady] = myfun(x, params)
   y = f(x,params)        % x is the variable, params are the parameters
if nargout >1 
   grady = f'(x,params);  % f' gradient of y wrt x
end

And now I create the subfunction you alluded to as

function [x,fval,exitflag,output] = runnested(x0,params,options)
%  
[x,fval,exitflag,output] = fminunc(@nestedfun,x0,options);
%
    function [y grady] = nestedfun(x)
        [y grady] = myfun(x,params);
    end
end

And finally, the optimization

    params= ['any desired values'];
    options = optimset('Display','iter','MaxIter',100,'GradObj','on'); 
    [x,fval,exitflag,output] = runnested(x0,net,options);

And MATLAB thows the following

??? Error using ==> uminus Too many output arguments. ... Caused by: Failure in initial user-supplied objective function evaluation. FMINUNC cannot continue.

Not quite sure what else I could try next.

Thanks

Answer 5

[Steve Grikschat]

We've yet to see your code for the analytical gradient calculation (hopefully we don't ;) ). I suspect that the error might be there.

Have you tried calling the function with two outputs as Alan suggested? i.e.

params = ...
f = @(x) myfun(x,params);
[fval0,grad0] = myfun(x0);

What do you get there?

Answer 6

[Javer]

I am not quite sure I am following you both not. If I follow your suggestion

params = ...
f = @(x) myfun(x,params);
[fval0,grad0] = myfun(x0);

Matlab doesn't like and says that Input argument "params" is undefined.

f(x0)

works OK but only returns the objective function (not the derivative).

[fval0,grad0] = f(x0,params);

fails with 'Too many output arguments' And

[fval0,grad0] = myfun(x0,params);

works OK and return the function and its derivatives. But I am left with an analytical derivative which I can't use with the large scale algorithm.

[Steve Grikschat]

Let's go back to the nested function example you wrote a few posts back. From the error it appears to me that the problem lies inside the function with a computation involving unary minus (uminus) or negation.

Try using the debugger to step into the 1st evaluation of your objective and gradient function from within fminunc to see where the error lies.

If you're not familiar, see the help here:

http://www.mathworks.com/help/techdoc/matlab_env/brqxeeu-175.html