Mathematical Sciences Department Financial Math Seminar: Forrest Miller, Northeastern

Title: The (Potential) Power of Applied Global Polynomial Optimization

Abstract:  In this talk, I will introduce the global optimization of polynomial objectives with polynomial constraints. I will describe how problems in portfolio selection can be framed as polynomial optimization problems, giving rise to a new toolbox to solve these problems to global optimality through the use of a sequence of semidefinite relaxations that grow in size. I will then discuss the benefits of solving these problems algorithmically, as well as challenges that this area currently faces. Unfortunately, it is quite simple to design and encounter problems in the real world where this general problem framework can struggle to reach optimality. However, recent work in robotics has shown that these challenges can be overcome for specific problem designs. Specifically, the deployment of redundant constraints has been observed to improve the performance of the semidefinite relaxations. 
I will conclude by showing some preliminary results I am developing on redundant constraint generation to improve the exactness of the convex (semidefinite) relaxations of these large-scale polynomial optimization problems