Fminunc gives Hessian with NaN

I am running a minimisation problem using fminunc but I get an Hessian matrix with NaN values. Could you help me to understand:

1) Why?

2) Which sort of underlying problem in my routine does it highlight?

3) How can I fix it (if fixable)

Note the the starting values have been accurately chosen among many as inducing the lowest function value when running fminunc

Here my code

clear 
rng default
load matrices
 
global L suppsize_X R absdiff epsilon V n YX_product

options = optimoptions(@fminunc, 'OptimalityTolerance', 1e-10, 'StepTolerance', 1e-10 ,'Display','off');
[paramhat,fval,exitflag, ~, grad, hessian]=fminunc(@obj_function_smoothed,coeff, options);
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function lik=obj_function_smoothed(coeff)
global L suppsize_X R absdiff epsilon V n YX_product
 
beta1=coeff(1); 
beta2=coeff(2); 
beta3=coeff(3); 
beta4=coeff(4); 
log_sigma_sq=coeff(5);
 
integral_component=zeros(((L+1)*suppsize_X),R);                      
lambda=0.05;
 
for r=1:R
    payoff_temp_exp=exp((beta1*absdiff(:,1)+beta2*absdiff(:,2)+beta3*absdiff(:,3)+beta4*absdiff(:,4)+epsilon(:,r)+sqrt(exp(log_sigma_sq))*V(:,r))/lambda); %((L+1)*suppsize_X)x1
    denom_temp=sum(reshape(payoff_temp_exp,L+1, suppsize_X)); %1 x suppsize_X
    denom_temp2=repmat(denom_temp, L+1,1); %(L+1) x suppsize_X
    denom=reshape(denom_temp2, (L+1)*suppsize_X,1); %((L+1)*suppsize_X)x1
    integral_component(:,r)=payoff_temp_exp./denom; %((L+1)*suppsize_X)x1
end
 
integral=sum(integral_component,2)/R;
 
integral_sample=repmat(integral,n,1);
 
lik=-sum(log(integral_sample).*YX_product)/n; 
 
end

[Laureen de Barsy]

Dear CT, I have a similar problem. Did you or someone else find an answer to the above question? Thank you!

Answer 1

[Matt J]

It is likely due to the objective function having an infinite value at the point being evaluated.

I notice the posted objective has exp(z) operations, which can easily overflow to Inf if the input z is too large. Similarly, it can underflow to zero if z-->-Inf which, if if it then becomes the input to the log() operations further downstream in the code, can also generate Infs.