Possible inconsistency in documentation of scipy brent minimization routine

Oleg Zolotov <[email protected]> Mon, 21 Aug 2023 23:55:30 +0300
Newsgroups gmane.comp.python.scientific.devel
Message-ID <[email protected]>
Dear SciPy developers,

the section 'Notes' of documentation page on Brents's minimization method
( https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.brent.html ) states that it ''Uses inverse parabolic interpolation when possible to speed up convergence of golden section method".

I belive this statement is not correct. There are actually two Brent's methods: one is to find a root (i.e., zero) of a function, and another one is to search a minima of a function (see a description in https://maths-people.anu.edu.au/~brent/pd/rpb011i.pdf  ).

According to the original description, Brent's optimization method is a combination of golden section search and successive parabolic interpolation (see, e.g., page 79, Section 8 of https://maths-people.anu.edu.au/~brent/pd/rpb011i.pdf ) 

As far as I know, inverse parabolic interpolation is used to find a root of a function. Because Brent's optimization method is a derivative-free method, the inverse parabolic interpolation can not be used 'under-the-hood' of Brent's method  to find a minima / maxima of a function.

Regards,
Oleg V. Zolotov

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