Rates of convergence for the continuum limit of nondominated sorting

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 equa...

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Bibliographic Details
Published in:arXiv.org 2022-05
Main Authors: Cook, Brendan, Calder, Jeff
Format: Article
Language:English
Subjects:
Convergence
Euclidean geometry
Euclidean space
Hamilton-Jacobi equation
Maximum principle
Multiple objective analysis
Optimization
Online Access:Get full text
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Summary: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.
ISSN:2331-8422