Why does fmincon not provide hessian option for sqp algorithm?

I know the hessian option is available for solvers such as the interior-point method. Also, providing a hessian is generally a faster (and more accurate) way to solve a problem than computing it via finite differences. Why then this choice?

Answer 1

[Matt J]

The SQP algorithm does not compute the Hessian via finite differences. It does, however, require a positive definite approximation of the Hessian (of the Lagrangian) and has some special steps to obtain that. If SQP permitted the user to supply a pre-calculated Hessian matrix, the matrix would need to be analyzed by the code and modified somehow to ensure positive definiteness.

[Chaitanya Awasthi]

Ok, that makes sense. Thank you!