[Octave-bug-tracker] [bug #57113] fminunc return wrong Hessian matrix

[Rik]

Follow-up Comment #10, bug #57113 (project octave):

fminunc is implemented in an m-file so experiments are pretty easy to make. 
Note this code at the end of the function:


  ## When info != 1, recalculate the gradient and Hessian using the final x.
  if (nargout > 4 && (info == -1 || info == 2 || info == 3))
    grad0 = grad;
    if (has_grad)
      [fval, grad] = fcn (reshape (x, xsz));
      grad = grad(:);
    else
      grad = __fdjac__ (fcn, reshape (x, xsz), fval, typicalx, cdif)(:);
    endif

    if (nargout > 5)
      ## Use the damped BFGS formula.
      y = grad - grad0;
      sBs = sumsq (w);
      Bs = hesr' * w;
      sy = y' * s;
      theta = 0.8 / max (1 - sy / sBs, 0.8);
      r = theta * y + (1-theta) * Bs;
      hesr = cholupdate (hesr, r / sqrt (s' * r), "+");
      hesr = cholupdate (hesr, Bs / sqrt (sBs), "-");
    endif
    ## Return the gradient in the same shape as x
    grad = reshape (grad, xsz);
  endif

  ## Restore original shapes.
  x = reshape (x, xsz);

  if (nargout > 3)
    output.iterations = niter;
    output.successful = nsuciter;
    output.funcCount = nfev;
  endif

  if (nargout > 5)
    hess = hesr'*hesr;
  endif


So there is specific code that calculates the Hessian at the final value of x.
 One issue, is that the gradient and Hessian aren't calculated when info == -3
which is also an error condition.  Maybe the test condition should be updated
to "info != 1".

Second, the calculation uses the damped BFGS formula and the damping will mean
that the Hessian only slowly changes over to the true value.  It seems like
this would be the location to insert a different Hessian calculation
algorithm.


    _______________________________________________________

Reply to this item at:

  <https://savannah.gnu.org/bugs/?57113>

_______________________________________________
  Message sent via Savannah
  https://savannah.gnu.org/