Convergence Rates and Semiconvexity Estimates for the Continuum Limit of Nondominated Sorting
Tuesday, October 22, 2019 - 1:25pm - 2:25pm
Brendan Cook (University of Minnesota, Twin Cities)
Multiobjective optimization problems are ubiquitous in science and engineering contexts, and nondominated sorting is a sorting process fundamental to multiobjective optimization. Recently proposed approaches to nondominated sorting exploit an underlying PDE that arises in the continuum limit. The need for theoretical guarantees for nondominated sorting algorithms motivates the problem of finding rates of convergence for the continuum limit. In this talk I will introduce PDE techniques from the theory of viscosity solutions and show how they can be used to solve this problem. Furthermore, I will show how semiconvexity estimates can be used to bolster convergence rates, and discuss approaches to obtaining semiconvexity estimates. This talk is intended to be entirely self-contained, so no prior knowledge of PDE will be assumed.