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Calculation of the gradient of a function in BFGS Quasi-Newton Algorithm

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Ahmed Nasr
Ahmed Nasr on 27 May 2020
Edited: Matt J on 29 May 2020
I have a function that I want to minimize using the BFGS Quasi-Newton algorithm.
If .
are given.
Also, A is given, B is not given, and C is a function of B only.
If I want to calculate to the gradient of the function (). Should I calculate it with respect to all variables or with respect to B only?

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Matt J
Matt J on 27 May 2020
With respect to all the variables that are unknown.

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Matt J
Matt J on 28 May 2020
You should take the gradient with respect to both B and C and then apply the Chain Rule:
Ahmed Nasr
Ahmed Nasr on 28 May 2020
I have a constraint that B*C > 0 .. But, I usually in my algorithm code substitute C by its function of B and take the gradient over B only as after replacing C with its function of B, B is considered as the only unknown variable in the function. Is that true?
Matt J
Matt J on 28 May 2020
It can be true. Or you can treat B and C as separate unknowns subject to an equality constraint,
C-g(B)=0
where g() is the function relating C to B. But it may make the optimization algorithm slower if it has to deal with additional variables and constraints.

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