Rates of convergence for the continuum limit of nondominated sorting
Analysis of PDEs
2022-05-18 v3 Probability
Abstract
Nondominated sorting is a discrete process that sorts points in Euclidean space according to the coordinatewise partial order, and is used to rank feasible solutions to multiobjective optimization problems. It was previously shown that nondominated sorting of random points has a Hamilton-Jacobi equation continuum limit. We prove quantitative error estimates for the convergence of nondominated sorting to its continuum limit Hamilton-Jacobi equation. Our proof uses the maximum principle and viscosity solution machinery, along with new semiconvexity estimates for domains with corner singularities.
Keywords
Cite
@article{arxiv.2006.05953,
title = {Rates of convergence for the continuum limit of nondominated sorting},
author = {Brendan Cook and Jeff Calder},
journal= {arXiv preprint arXiv:2006.05953},
year = {2022}
}