Brent's Minimization Method

Chapters:
0:00 Intro
0:16 Scaffolding
0:31 Motivation
1:17 Parabolic Interpolation Review
1:48 Renaming Variables
2:40 Brent's Method Algorithm
3:19 SPI Behaving?
4:08 Note on Updating
4:38 Brent's Method Visualization
6:02 Numerical Example
6:29 Note on Steps
6:43 MATLAB fminbnd
7:12 Minimum Strategy - Derivative
7:49 Note on Convergence Order
8:04 Oscar's Notes
8:39 Outro

Suggested Viewing:

References:

Background music "The Golden Present" by @JesseGallagher

#GoldenSectionSearch #SuccessiveParabolicInterpolation #NumericalAnalysis

[AJ-etvf]

Awesome video man! Love your videos about numerical analysis as a numerical analysis enthusiast! You cover algorithms for solving nonlinear equations (and minimization it's related cousin) that aren't usually covered in most/usual numerical analysis channels.

[martingarciavazquez]

Thank you very much for posting this video, I found it incredibly useful!

[alexandrevachon]

All of the minimization techniques that were described in this series work not just with unimodal functions, but also with *multimodal* functions. They can also be used to find critical points.

[houywsb]

Thanks for your videos! I like the way of your explanations via visual illustrations, that's really helpful. Also it's great that you refer to the history of algorithms which you are exploring. Are you planning to record some videos about multidimensional minimization methods, starting from basic things and then, for example, exploring the algorithm?

[alexandrevachon]

I think I found something related to minimization, something about the Nelder-Mead method and Powell's method. I think these should be worth exploring. I wonder if there's not only just combining both golden section search and successive parabolic interpolation, but also the latter with dichotomous search, ternary search or Fibonacci search... These three methods are also guaranteed to find the result. But they are slower than successive parabolic interpolation or Brent's minimization method. But it would be worth a try.

[tszhinchan]

Thank you for your great tutorial. May I know how we can compute p and q stated in the video?

[johnphilmore]

Hey Oscar! Question:
Where does the (3-sqrt(5))/2 come from at 2:50? That would mean that v, w, x are all bigger than b when initialing the method. That doesn’t seem right, but I may be wrong