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 [ Ссылка ]
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 [ Ссылка ]
Dichotomous Search [ Ссылка ]
Fibonacci Search [ Ссылка ]
Jarratt's Method - Successive Parabolic Interpolation [ Ссылка ]
Brent's Minimization Method [ Ссылка ]
Minimization Playlist [ Ссылка ]
Two opposite games involving golden ratio (ft. Tom Rocks Maths) by @mathemaniac [ Ссылка ]
References:
Algorithms for Minimization without Derivatives by Richard P. Brent [ Ссылка ]
Optimum Seeking Methods by Douglass Wilde [ Ссылка ]
Sequential Minimax Search for a Maximum by J. Kiefer [ Ссылка ]
Best Exploration for Maximum is Fibonaccian by S. M. Johnson [ Ссылка ]
Background music "The Golden Present" by @JesseGallagher
#GoldenSectionSearch #NumericalAnalysis
