Error in fminunc function

The problem I'm having is that when I call the fminunc function it doesn't solve the problem because it sayd that the gradient is zero and that it needs two elements, but when I just call the gradient it throws the right one. What am I doing wrong? Please help me :)

This is the script

function [f,grad,hess] = exam_sylvi(x)
f = 2*x(1)+3*x(2)^2+exp(2*x(1)^2+x(2)^2);
if nargout > 1
    grad = gradient (f,[x(1),x(2)])
end
if nargout > 2

      hess = hessian (f,[x(1),x(2)])
  end
  end

This is the run

EDU>> grad

grad =

   4*x1*exp(2*x1^2 + x2^2) + 2
       2*x2*exp(2*x1^2 + x2^2)

EDU>> hess

hess =

[ 4*exp(2*x1^2 + x2^2) + 16*x1^2*exp(2*x1^2 + x2^2),                       8*x1*x2*exp(2*x1^2 + x2^2)]
[                        8*x1*x2*exp(2*x1^2 + x2^2), 2*exp(2*x1^2 + x2^2) + 4*x2^2*exp(2*x1^2 + x2^2)]

EDU>> [x,fval,exitflag] = fminsearch(@exam_sylvi,[1,0])

x =

     -0.3766   -0.0000

fval =

      0.5748

exitflag =

       1

EDU>> options = optimoptions('fminunc','Display','iter','Algorithm','quasi-newton','HessUpdate','steepdesc','GradObj','on');
EDU>> [x,fval,exitflag,output] = fminunc(@exam_sylvi,[1,0],options)

grad =

       0

Error using fminunc (line 339)
User-defined objective gradient does not have the correct number of elements:
the gradient should have 2 elements.

Answer 1

[Walter Roberson]

Your tests are with symbolic x, but fmincon runs with numeric x. So f = 2*x(1)+3*x(2)^2+exp(2*x(1)^2+x(2)^2) is going to produce a numeric scalar because x(1) and x(2) will have particular numeric values. You then apply the numeric gradient function to that scalar, giving the x(1) and x(2) as the step sizes (which is obviously wrong), but since f is only a scalar the step sizes are irrelevant and the numeric gradient is going to return just the scalar.

What you should probably do is

function [f,grad,hess] = exam_sylvi(x)
  syms x1 x2
  F = 2*x+3*x2^2+exp(2*x1^2+x2^2);
  f = double( subs(F, [x1 x2], x) );
  if nargout > 1
      grad = double( subs( gradient(F,[x1, x2]), [x1, x2], x) );
  end
  if nargout > 2
        hess = double( subs( hessian(F,[x1, x2]), [x1, x2], x) );
  end
end

Except, of course, that would be inefficient and you would be better to pre-calculate those before calling fmincon:

    syms x1 x2
    F = 2*x+3*x2^2+exp(2*x1^2+x2^2);
    fh = matlabFunction(F, 'vars', {x1, x2});
    gradh = matlabFunction( gradient(F, [x1, x2]), 'vars', {x1, x2});
    hessh = matlabFunction( hessian(F, [x1, x2]), 'vars', {x1, x2});

    [x,fval,exitflag,output] = fminunc(@(x) exam_sylvi(x, fh, gradh, hessh), [1,0], options)

Together with

function [f, grad, hess] = exam_slvi(x, fh, gradh, hessh)
  f = fh(x);
  if nargout > 1
    grad = gradh(x);
  end
  if nargout > 2
    hess = hessh(x);
  end
end