Which method is implemented in fmincon (interior-point) when it is supplied with the gradient and the bfgs-Hessian and has only box constraints?

I would like to use fmincon (interior-point) in my paper with the following options:

options = optimoptions('fmincon','Algorithm','interior-point', 'Hessian','bfgs','GradObj','on','Display','off','MaxIter',max_iter,'TolFun',1e-4,'TolX',1e-4);

I would like to cite the paper that proposes the method with the above set of options in my paper. Which method in the literature fmincon uses with this set of options? It does not make sense to say here interior-point method, since I am not using general inequality constraints, but simple box-constraints. So I guess it is a Quasi-Newton method using the 'bfgs' technique to approximate the Hessian, which uses projection operators in order satisfy the box constraints per-iteration. The point is that there are many papers doing the same thing, and I do not know which one you implement.

Thank you very much in advance!

[Matt J]

The tolerances 'TolFun',1e-4,'TolX',1e-4 look suspiciously loose. Are you sure these are giving you good results?

Answer 1

[Matt J]

I would like to cite the paper that proposes the method with the above set of options in my paper.

The interior-point method documentation provides some literature references.

So I guess it is a Quasi-Newton method using the 'bfgs' technique to approximate the Hessian, which uses projection operators in order satisfy the box constraints per-iteration.

No, I don't think so. There is nothing in the documentation about simple bounds being treated as a distinct case. Also, that strategy would not be convergent unless the projection was done with respect to the Hessian-induced norm, so there is no simplicity to be gained by treating that case separately.