Why does fmincon not provide hessian option for sqp algorithm?

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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?

Accepted Answer

Matt J
Matt J on 12 Apr 2021
Edited: Matt J on 12 Apr 2021
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.

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