Golden-section Search

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 https://www.github.com/osveliz/numeri... 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    • Ternary Search   Dichotomous Search    • Dichotomous Search   Fibonacci Search    • Fibonacci Search   Jarratt's Method - Successive Parabolic Interpolation    • Successive Parabolic Interpolation - Jarra...   Brent's Minimization Method    • Brent's Minimization Method   Minimization Playlist    • Minimization   Two opposite games involving golden ratio (ft. Tom Rocks Maths) by ‪@mathemaniac‬    • Two opposite games involving golden ratio ...   References: Algorithms for Minimization without Derivatives by Richard P. Brent https://maths-people.anu.edu.au/~bren... Optimum Seeking Methods by Douglass Wilde https://archive.org/details/optimumse... Sequential Minimax Search for a Maximum by J. Kiefer https://www.jstor.org/stable/2032161 Best Exploration for Maximum is Fibonaccian by S. M. Johnson https://apps.dtic.mil/dtic/tr/fulltex... Background music "The Golden Present" by ‪@JesseGallagher‬ #GoldenSectionSearch #NumericalAnalysis