Can I supply a gradient to fmincon when my objective function is anonymous?

I am using fmincon and would like to supply a gradient for the objective function to speed up convergence. The trouble is I use an anonymous objective function so I can pass parameters to my real objective function. I believe the anonymous function only picks up the first argument of my real objective function, which is the function value and not the gradient. The basic structure of my code is:

if true
%%%%%%%%%%%%%%%%%%%
[f,gradf]=realobjective(parameters,x]
f=blah;
gradf=blah;
end
%%%%%%%%%%%%%%%%%%%
options=optimoptions(@fmincon,'Algorithm','active-set','MaxFunEvals',1E5,'MaxIter',1E5,'TolFun',1E-6,'TolX',1E-6,'GradConstr','on','GradObj','on');
xguess=0;
func=@(x)realobjective(parameters,x)
argmin=fmincon(func,xguess,[],[],[],[],0,1000,nonlconstr,options)
end

So I think fmincon is not using the gradient I have defined in the real objective function. I'd be incredibly grateful for any advice.

David

[Rustem Devletov]

Hey, friend! I'm a fourth year student in Russia, currently writing my thesis. My supervisor asked me to provide gradient to fmincon

I have triend smth like this

function F = rosenbrockwithgrad(x)

F = 100*(x(2) - x(1)^2)^2 + (1-x(1))^2;

if nargout > 1 % gradient required

g = [-400*(x(2)-x(1)^2)*x(1)-2*(1-x(1));

200*(x(2)-x(1)^2)];

end

But he said that he wants it to be found in another file. How can I implement this? How do I find gradient in one file and pass it to another one?

Answer 1

[Matt J]

What you've posted looks fine. Call nargout inside realobjective (e.g., at a breakpoint), to test whether fmincon is calling it with two output arguments.

[Yu Jiang]

I believe Matt is correct. func should generate two outputs as expected. More details regarding anonymous function can be found via the following link:

http://www.mathworks.com/help/matlab/matlab_prog/anonymous-functions.html

-Yu Jiang

[Matt J]

On second thought, have nargout printed to the screen at every call to realobjective throughout the optimization process and check whether it ever goes above 1.

      [f,gradf]=realobjective(parameters,x]
      f=blah;
      gradf=blah;

        disp(['NARGOUT=' num2str(nargout)])   %inserted for debugging

      end

You can't be sure fmincon will call with nargout=2 all the time. There may be some steps in the algorithm that require a function evaluation, but not a gradient evaluation (e.g., line searches).

[DavidZ]

one small comment to my point below: it does work with grad objective function on, but not with grad constraint on! I've double checked and am sure the derivatives for my constraint are correct. Hrm! Anyway it is A LOT quicker now 3.5secs vs 70secs so I'm happy with that:)

[Matt J]

Did you try running with 'DerivativeCheck' set to 'on' to validate your gradient calculation? Sounds like your constraint gradient calculation is working okay, but the objective function gradient calculation might have errors.

[Rustem Devletov]

Hey, friend! I'm a fourth year student in Russia, currently writing my thesis. My supervisor asked me to provide gradient to fmincon

I have triend smth like this

function F = rosenbrockwithgrad(x)

F = 100*(x(2) - x(1)^2)^2 + (1-x(1))^2;

if nargout > 1 % gradient required

g = [-400*(x(2)-x(1)^2)*x(1)-2*(1-x(1));

200*(x(2)-x(1)^2)];

end

But he said that he wants it to be found in another file. How can I implement this? How do I find gradient in one file and pass it to another one?

Answer 2

[DavidZ]

Thanks both. It's very mysterious; when I turn the gradient calls off fmincon does converge (slowly) to the right answer (I know it's right as for certain parameter values I can work out an analytical solution to compare to the numerical solution fmincon gives) but when I turn the gradient calls on it never converges. I tried the debugging tip Matt helpfully suggested and fmincon is calling withing nargout 2 some of the time, but not all of it. Any thoughts? Thanks again for your help.