Why does fmincon not provide hessian option for sqp algorithm?

Question

Chaitanya Awasthi 2021-4-12

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评论： Chaitanya Awasthi 2021-4-12

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?

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Answer 1

Matt J 2021-4-12

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https://ww2.mathworks.cn/matlabcentral/answers/800166-why-does-fmincon-not-provide-hessian-option-for-sqp-algorithm#answer_673586

编辑：Matt J 2021-4-12

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.