Using Hessian for least squares problem

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It looks like lsqnonlin() from MatLab can't make use of a Hessian (it is not stated explicitly by MatLab, but I read this in the article "Optimization and uncertainty analysis of ODE models using 2nd order adjoint sensitivity analysis" by P. Stapor and others). I want to use fminunc() that is able to make use of a Hessian. I produce the current curve derivatives for all involved points with MatLab Symbolic Toolbox, but I have to program objective function evaluation from the single point deriavtives. The article "Using Symbolic Mathematics with Optimization Toolbox™ Solvers" in MatLab documentation does not help because of programming involved in my case. Using a MatLab function for the objective function would require making the symbolic functions details to be available to this function. Then I need to make global all the symbolic functions involved which is not ideal. Does anyone know a better way to attack my problem?
Valeri Aronov
Valeri Aronov on 6 Jun 2021
Edited: Valeri Aronov on 31 Aug 2021
1) Thanks, Alex. Your suggestion seems to be exactly what I am looking for. May I accept your answer once I test the suggested solution?
2) Thanks, John.
"... I see people want to emulate ...". Not I, John. In fact, I read one paragraph only from the whole paper about lsqnonlin() and Hessian, because that is what I was asking Google for.

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Accepted Answer

J. Alex Lee
J. Alex Lee on 6 Jun 2021
Now that the actual question is clarified as a coding question and not a math question, it seems these should help:

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