Open Lecture — Across the Watershed: Unifying Perspectives on Optimization

Mathematical optimization is an enabling technology with many applications across science and engineering, including operations research, machine learning, robotics and control.

Conventional wisdom classifies optimization problems and techniques along several different branches (discrete/continuous, convex/non-convex, etc.), often with little overlap and cross-fertilization. In the first part of the talk, I review and revisit this classical viewpoint. I will then argue that often these differences are illusory, and perhaps much less significant than we previously thought. In particular, I will explain how the algebraic-geometric perspective of sum of squares methods provides a much needed common foundation and understanding, as well as novel applications and state-of-the art algorithms.

The talk will be self-contained, and will provide a gentle introduction to this exciting research area, emphasizing geometric intuition and surveying some recent developments. No specific knowledge about optimization will be assumed!

Light refreshments will be served before the lecture at 3:30 p.m.