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

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Ahmed Nasr 2020-5-27

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编辑： Matt J 2020-5-29

采纳的回答： Matt J

I have a function

that I want to minimize using the BFGS Quasi-Newton algorithm.

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 2020-5-27

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With respect to all the variables that are unknown.

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 2020-5-28

编辑：Matt J 2020-5-29

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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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