Why do the elements of my user-provided numerical Jacobian seem to change when compared with Matlab's using the 'DerivativeCheck' option?

I am using fmincon to solve a constrained optimisation problem.

My problem involves 8900 design variables and has 5846 non-linear equality constraints (0 linear equality, 0 linear inequality and 0 non-linear inequality constraints). The non-linear equality constraints Jacobian has a known sparsity pattern which I am trying to exploit (avoid unnecessary computations to be performed by Matlab), and I am trying to numerically compute each of the terms using forward differences.

The non-linear equality constraints Jacobian has the following dimensions (5846 x 8900).

I am now in the process of checking my user-supplied Jacobian with that computed via Matlab through fmincon (fmincon options, 'DerivativeCheck','on').

I have performed the 'check' multiple times, and whilst my derivatives do not match exactly, the differences are small as indicated below:

(8885,2566)

user: -1.48538

matlab: -1.48454

diff: 0.000564995

(8882,3898)

user: -2.13046

matlab: -2.1299

diff: 0.000263211

(8885,2714)

user: -0.469954

matlab: -0.470041

diff: 8.7738e-05

(8888,4934)

user: -0.876923

matlab: -0.877136

diff: 0.000213623

(8885,2640)

user: 0.61372

matlab: 0.613775

diff: 0.00050354

(8888,4934)

user: -0.342921

matlab: -0.343118

diff: 0.000196457

In some instances when I have checked the derivatives, my user-supplied value for element (8885,4900), for example, differs between instances when I run the function - I do not make changes to the values of the design variables.

Can someone please explain why I am noticing these differences in my own user-supplied Jacobian?

Kind regards,

Nicos Haralabidis