Michael Cohen and Self-Concordant Barriers Over L_p Balls

Explore the mathematical concepts of self-concordant barriers and L_p balls in this 34-minute lecture from the Michael Cohen Memorial Symposium at the Simons Institute. Delve into Yuanzhi Li's presentation, which covers the joint work and contributions of Michael Cohen. Examine self-concordant functions in one and high dimensions, understanding their local quadratic nature and importance. Investigate the concept of self-concordant barriers, focusing on their properties and applications. Learn about the "Largeness of the Dikin Ellipsoid" intuition and the main questions addressed in Cohen's research. Follow the proof ideas, including symmetric cases and Cohen's innovative approaches. Gain insights into the application of these concepts to general functions, enhancing your understanding of advanced mathematical topics in optimization and geometry.

Intro
Based on the joint work of
Some stories
Self-concordant functions in dimension one
Locally Quadratic
Self-concordant functions in high dimension
Why Self-concordant?
Yet Michael's another contribution
Self-concordant barriers
A good self-concordant barrier
Intuition "Largeness of the Dikin Ellipsoid"
Main Question
Michael's contribution
Proof idea
Proofidea (Symmetric)
Michael's idea (1)
Michael's idea (2)
Michael's proof
General functions