Golden-section Search

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:

References:

Background music "The Golden Present" by @JesseGallagher

#GoldenSectionSearch #NumericalAnalysis

[cangizer]

Thank you Oscar, those videos really helped me to understand and visualize what's going on. You're a life saver in terms of math for sure :)

[filip]

wow you explained this sooo much better than my lecturer

[blaise]

very useful, thanks! my CS101 teacher referred me here and it did not dissapoint! :)

[tetamusha]

Hey, thanks to you, I was able to implement these methods in a scientific package I work on and I got significant speedups and more stability in my results, compared to the janky solutions I used before. Thanks for the videos.

[vasantk]

These videos are very informative. Thank you!

[alexandrevachon]

Overall, my favorites are golden section search and successive parabolic interpolation.

[niravtank]

Video is very informative and thank you for that. Can you please explain derivation of golden section ratio more? I mean to say..I cannot correlate that how you managed to keep same ratio by for every iteration.. It seems you took ratio of current lengths only..

[orktv]

If we are looking for an inflection point rather than an extremum, it appears we need to draw two auxiliary lines before we can rule out one of the outermost subintervals. We can re-use two of the lines and need to draw a third one to repeat the process. Is it still possible to choose the proportionate positioning of the lines in an efficient way like here? And if so, can we generalize this to n lines (to find the root of the n-1th derivative)?

[lizzyzhou]

Another thing that bothers me: Why the iteration times for Finonacci is one less than for golden-section? Is that always true? Then how can we prove that?

[esakkiappanthevar]

Could you please tell, what is the real-life application of the golden section search?