Uploaded July 2020 | Updated September 2026, 1 week ago
Golden-section Search is a minimization algorithm that expands on the Fibonacci Search scheme described by J. Kiefer and S. M. Johnson. This interval-based numerical method improves on Ternary Search and Dichotomous Search be reusing interval points based on the golden ratio (phi). Code can be found on GitHub github.com/osveliz/numerical-veliz
Chapters
0:00 Intro
0:23 Algorithms for Minimization without Derivatives
0:43 Optimum Seeking Methods
1:34 Ternary Recap
2:04 Reusing Points
2:22 Finding c
2:45 Fixed Constant Ratio
3:28 Computing c
3:58 Golden-section Search Algorithm
4:47 GSS Visualized
5:31 Numerical Example
5:55 Comparing Methods
6:18 Search Space Shrinkage
7:01 Golden Ratio Extra History
7:28 Properties of φ
8:13 Oscar's Notes
8:38 Mathemaniac
8:49 Thank You
Suggested Viewing:
Ternary Search youtu.be/7h86n97naH4
Dichotomous Search youtu.be/n_zefNBfhSM
Fibonacci Search youtu.be/GAafWFRGP7k
Jarratt's Method - Successive Parabolic Interpolation youtu.be/3WHcQofG7B8
Brent's Minimization Method youtu.be/BQm7uTYC0sg
Minimization Playlist youtube.com/playlist?list=PLb0Tx2oJWuYIXLHAjQgko2fZtJ_NxnV-x
Two opposite games involving golden ratio (ft. Tom Rocks Maths) by @mathemaniac youtu.be/UOAylfclg14
References:
Algorithms for Minimization without Derivatives by Richard P. Brent https://maths-people.anu.edu.au/~brent/pub/pub011.html
Optimum Seeking Methods by Douglass Wilde archive.org/details/optimumseekingme00wild
Sequential Minimax Search for a Maximum by J. Kiefer jstor.org/stable/2032161
Best Exploration for Maximum is Fibonaccian by S. M. Johnson https://apps.dtic.mil/dtic/tr/fulltext/u2/224385.pdf
Background music "The Golden Present" by @JesseGallagher
#GoldenSectionSearch #NumericalAnalysis
Golden-section Search is a minimization algorithm that expands on the Fibonacci Search scheme described by J. Kiefer and S. M. Johnson. This interval-based numerical method improves on Ternary Search and Dichotomous Search be reusing interval points based on the golden ratio (phi). Code can be found on GitHub github.com/osveliz/numerical-veliz
Chapters
0:00 Intro
0:23 Algorithms for Minimization without Derivatives
0:43 Optimum Seeking Methods
1:34 Ternary Recap
2:04 Reusing Points
2:22 Finding c
2:45 Fixed Constant Ratio
3:28 Computing c
3:58 Golden-section Search Algorithm
4:47 GSS Visualized
5:31 Numerical Example
5:55 Comparing Methods
6:18 Search Space Shrinkage
7:01 Golden Ratio Extra History
7:28 Properties of φ
8:13 Oscar's Notes
8:38 Mathemaniac
8:49 Thank You
Suggested Viewing:
Ternary Search youtu.be/7h86n97naH4
Dichotomous Search youtu.be/n_zefNBfhSM
Fibonacci Search youtu.be/GAafWFRGP7k
Jarratt's Method - Successive Parabolic Interpolation youtu.be/3WHcQofG7B8
Brent's Minimization Method youtu.be/BQm7uTYC0sg
Minimization Playlist youtube.com/playlist?list=PLb0Tx2oJWuYIXLHAjQgko2fZtJ_NxnV-x
Two opposite games involving golden ratio (ft. Tom Rocks Maths) by @mathemaniac youtu.be/UOAylfclg14
References:
Algorithms for Minimization without Derivatives by Richard P. Brent https://maths-people.anu.edu.au/~brent/pub/pub011.html
Optimum Seeking Methods by Douglass Wilde archive.org/details/optimumseekingme00wild
Sequential Minimax Search for a Maximum by J. Kiefer jstor.org/stable/2032161
Best Exploration for Maximum is Fibonaccian by S. M. Johnson https://apps.dtic.mil/dtic/tr/fulltext/u2/224385.pdf
Background music "The Golden Present" by @JesseGallagher
#GoldenSectionSearch #NumericalAnalysis
