Cut Generating Functions

Explore the theory of cut generating functions in mixed integer programming through this 41-minute lecture. Delve into the fundamental concepts and discover how this tool automatically derives cutting planes. Examine the significance of subadditive functions, particularly those that are piecewise linear, and investigate the number of slopes in these functions. Learn about new findings in the field and consider open questions posed by the speaker. Gain insights into cutting planes, Gomory mixed integer cuts, minimal functions, and the comparison between finite and infinite models in one dimension. Understand the relationship between minimality and extremality in the context of cut generating functions.

Intro
Cutting planes
Gomory mixed integer cuts
Cut generating functions
GMI cut as a valid function
Minimal functions
GMI cuts are minimal valid functions
Are extreme functions always nice?
Number of slopes of extreme functions
Let's discretize
Minimality and extremality
Finite vs infinite model (1-dim)
Questions