Polyhedral Geometry of Pivot Rules

Explore the geometric perspective on pivot rules in linear programming through this 30-minute lecture. Delve into the relationship between linear programs and polyhedra, examining how simplex methods create arborescences on oriented graphs. Discover how certain pivot rules can be associated with polytopes that capture these arborescences, and investigate their connections to shadow-vertex-rules, monotone path polytopes, and polytopes from geometric combinatorics. Learn about the collaborative research conducted with Alex Black, Jesús De Loera, and Niklas Lütjeharms, presented by Raman Sanyal at the Hausdorff Center for Mathematics.