fmincon check Hessian (in DerivativeCheck)

When I set opts.DerivativeCheck='on' in fmincon, it checks only the gradient. How do I tell it to check the Hessian as well?

EDIT: My options

          opts = optimset();
          opts.MaxIter = 1e4;
          opts.MaxFunEvals = 1e6;
          opts.TolFun = 1e-4;
          opts.Algorithm = 'interior-point'; % 'trust-region-reflective'
          opts.GradObj = 'on';
          opts.GradConstr = 'on';
          opts.DerivativeCheck = 'on';
          opts.Diagnostics = 'on';
          opts.Display = 'iter';
          %opts.Display = 'none';
          opts.FinDiffType = 'central';
          if 1
              opts.HessMult = fH;
              opts.Hessian = 'user-supplied';
              %opts.Hessian = 'fin-diff-grads';
              opts.SubproblemAlgorithm = 'cg';
          else
              opts.Hessian = 'lbfgs';
          end

Answer 1

[Matt J]

I don't think you can, but an indirect way would be to run like below with MaxIter=1 and have fmincon return the Hessian with the 'Hessian' option turned both on and off. Then you can check the Hessian error manually.

I agree it is counter-intuitive, but I think it might be deliberate that the DerivativeCheck does not test the Hessian. Often, minimization algorithms will work with fairly crude approximations to the Hessian, so maybe it is expected that your user-supplied Hessian will not always be exact. Or, maybe it is with large dimensional problems in mind, where finite difference derived Hessians are too expensive to compute, even for testing purposes, but you still might want to use DerivativeCheck to verify the gradient.

Q=[2 1;1,2];
 Q=Q+Q.';

   opts=optimoptions(@fmincon,'DerivativeCheck','on',...
                              'GradObj','on','Hessian','off','MaxIter',1);
  [x,fval,exitflag,output,lambda,grad,H_off]=...
      fmincon(@(x)objfun(x,Q),[1,2],[],[],[],[],[-1,-1],[1,1],[],opts)

   opts=optimoptions(@fmincon,'DerivativeCheck','on',...
                              'GradObj','on','Hessian','on','MaxIter',1);

[x,fval,exitflag,output,lambda,grad,H_on]=...
    fmincon(@(x)objfun(x,Q),[1,2],[],[],[],[],[-1,-1],[1,1],[],opts)

HessianError=H_on-H_off
keyboard

function [f,g,H]=objfun(x,Q)

   x=x(:);

   f=x.'*Q*x/2;
   g=Q*x;
   H=eye(2);

[Zohar]

Nice idea!