Explanation for formula calculating step size for finite difference used in fmincon

Question

Hainan Wang 2021-4-10

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https://ww2.mathworks.cn/matlabcentral/answers/798412-explanation-for-formula-calculating-step-size-for-finite-difference-used-in-fmincon

编辑： Matt J 2021-4-11

When I view the page of ‘fmincon’, one option in optimset is ‘FiniteDifferenceStepSize’. The descriptions are copied below:

FiniteDifferenceStepSize to a vector v, the forward finite differences delta are

delta = v.*sign′(x).*max(abs(x),TypicalX);

where sign′(x) = sign(x) except sign′(0) = 1. Central finite differences are

delta = v.*max(abs(x),TypicalX);

What's the meaning of v, x and typicalX in formula?

For example, I want to calculate the step size ‘delta’ for obtaining the gradient of objective function J with respect to variables u_i by forward finite difference method, i.e., for forward finite difference, partial J/partial u_i= [J(u1,u2,…,u_i + deltau_i,…, uend)-J(u1,u2,...,u_i,...,uend)]/deltau_i. I guess 'v' in formula is the u vector [u1, u2,...,uend]?? But what does x and TypicalX mean?

Thank you in advance!

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Answer 1

Matt J 2021-4-10

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https://ww2.mathworks.cn/matlabcentral/answers/798412-explanation-for-formula-calculating-step-size-for-finite-difference-used-in-fmincon#answer_672302

编辑：Matt J 2021-4-11

v is the value assigned to the optimoptions parameter FiniteDifferenceStepSize.
TypicalX is another optimoptions parameter whose default is a vector of ones.
x is the current vector of unknown optimization variables (you seem to be calling it u).