relative vs absolute first order optimality

Hi all, I have another question about first order optimality.

Consider the following code:

y = @(x) x^3+5*x+2;
y2 = @(x) x^2+5*x-4;

A = [-1; 1];
b = [5; 5];

const = @(x) [-x-5, x-5];

options.Algorithm = 'interior-point';
options.TolFun = 1e-6;
[optx, z, exitflag,output,lambda,grad,hessian] = fmincon(y,0,A,b,[],[],[],[], [],options);
[opt2x,z2,exitflag2,output2,lambda2,grad2,hessian2] = fmincon(y2,0,A,b,[],[],-100,100, [],options);

Okay, there's a cubic (not minimizable) and a quadratic (minimizable).

I know the default optimality tolerance is 1e-6 and algorithm is interior point, but just making sure.

output2.firstorderopt = 8.0111e-07 < 1e-6 :)

output.firstorderopt = 7.4865e-05 > 1e-6 :(

Now for the first case, if I click on the command window, I get this:

Local minimum found that satisfies the constraints.

Optimization completed because the objective function is non-decreasing in 
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.

<stopping criteria details>

Optimization completed: The relative first-order optimality measure, 9.358141e-07,
is less than options.OptimalityTolerance = 1.000000e-06, and the relative maximum constraint
violation, 0.000000e+00, is less than options.ConstraintTolerance = 1.000000e-06.

So the relative first order opt is less than 1e-6, but that's after dividing absolute by the gradient, which is equal to 80 (b/c the optimal point is at the boundary).

Okay, but there's still a conundrum because for the other case, where the optimal point is between the bounds, output2.firstorderopt is equal to the relative first order optimality I get from this message. I mean, if it divided absolute by the gradient, which is very close to 0, it would be in big trouble.

How does MATLAB decide which one to use, can I predict this before/after, and is there a way to force it to just use absolute optimality all the time?

[Benjamin Gibson]

So I found this:

https://www.mathworks.com/matlabcentral/answers/416519-inconsistent-data-in-fmincon-output-structure?s_tid=answers_rc1-2_p2_MLT

It suggests that the factor used is the first order optimality of the initial case. That doesn't seem like a very consistent termination condition to me. Wouldn't that mean your solver tries harder or not based on the quality of your initial guess? Or is this answer correct?