Open Problems & Diet Problems

I wrote this as a lecture series for the IPCO 2024 summer school. This is an abbreviated version. We discuss theoretical analysis about the simplex method for linear programming, and what stands between these analyses and understanding of our scientific question. Looking specifically at smoothed analysis, we discuss the realism of the theory and the obstacles that make experimental validation difficult. There is a long aside where we talk about the social and historical context of the diet problem, one of the most famous examples of linear programming. Specifically we learn about how this was used to advocate against the minimum wage, to structurally underfeed incarcerated people in prison and to justify an embargo on food during the siege on the Gaza Strip between 2007 and 2010. Footnotes and references: https://sophie.huiberts.me/videos/open-problems.html Music by Alec Lambert from Heaven Will Be Mine Timestamps: 00:00 Open problems in linear programming 07:37 The part where I talk about my mathematics 15:45 Diet problem 18:30 Minimum wage debate 24:29 Meal planning in USA prisons 29:35 Blockade of the Gaza Strip 2007 37:14 Human rights 42:26 What's in production