Dr. Dominique Zosso (Dept. of Mathematical Sciences, MS

10/22/2022  3:10pm

Abstract:

In this talk we present an entirely geometric proof of the well-established Lagrange- and KKT-theorems for first order optimality conditions in the case of convex objectives and constraints. We largely refrain from using calculus and linear algebra concepts, and provide all the geometric definitions and tools in a visually accessible, self-contained form, instead. Our work makes extensive use of convex geometry elements such as tangent cones, normal cones, and hyperplanes of support, to define the objective function's properties such as convexity and sub-gradient. As a result, we provide an illustrative approach to convex optimization, including helpful examples and counter-examples, overall supposedly accessible to students before formal calculus. This is joint work with Alexandra Emmons, Henry Fessler, and Ryan Grady.

This talk will be highly accessible and provide an illustrative overview of some of the topics to be taught in M362 "Linear Optimization" and M507 "Mathematical Optimization". Math undergraduate and graduate
students of all fields are encouraged to attend.