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A visual-heavy introduction to Linear Programming including basic definitions, solution via the Simplex method, the principle of duality and Integer Linear Programming. #some3 More problems: https://slama.dev/youtube/linear-programming-in-python/ Made as my entry to SoME3: https://3blue1brown.substack.com/p/some3-begins ------------------ Timetable: 0:00 - Introduction 0:26 - Basics 3:44 - Simplex Method 11:47 - Duality 14:01 - Integer Linear Programming 17:31 - Conclusion ------------------ Source code: https://github.com/xiaoxiae/videos/tree/master/18-lopt/ Music (in the order it appears in the video): ► Cases to Rest by Blue Dot Sessions: https://app.sessions.blue/browse/track/139762 ► Thannoid by Blue Dot Sessions: https://app.sessions.blue/browse/track/126782 ► ZigZag Heart by Blue Dot Sessions: https://app.sessions.blue/browse/track/31462 ► Maisie Dreamer by Blue Dot Sessions: https://app.sessions.blue/browse/track/31458 ► Night Light by Blue Dot Sessions: https://app.sessions.blue/browse/track/189819 Software used: ► Manim (animation software): https://github.com/ManimCommunity/manim/ ► Kdenlive (video cutting): https://kdenlive.org/en/ ► ffmpeg (audio/video processing): https://ffmpeg.org/ ► OBS (audio/video recording): https://obsproject.com/download ► arecord (audio recording): https://linux.die.net/man/1/arecord ► sox (audio processing): http://sox.sourceforge.net/ ► Inkscape (vector image editing): https://inkscape.org/ ► Midjourney (image generation): https://www.midjourney.com/app/ Social media: ► Website (for other things I'm up to): https://slama.dev/ ► Patreon (if you'd like to support me): https://www.patreon.com/YTomS Thanks to Matěj Kripner, Martin Balko, Lucia Zhang, Václav Rozhoň (@polylog), Kateřina Sulková, Mohit Shrestha, Teo Tuicu and Tomáš Sláma (my dad, not me) for valuable feedback. ------------------ [EN] Gerard Sierksma; Yori Zwols (2015). Linear and Integer Optimization: Theory and Practice https://www.taylorfrancis.com/books/mono/10.1201/b18378/linear-integer-optimization-gerard-sierksma-gerard-sierksma-yori-zwols [CZ] Přednáška Jiřího Sgalla: Lineární programování a kombinatorická optimalizace https://iuuk.mff.cuni.cz/~sgall/vyuka/LP/ [EN] George B. Dantzig (1982): Reminiscences about the origins of linear programming https://apps.dtic.mil/sti/pdfs/ADA112060.pdf