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

  1. viscosity solutions
  2. partial differential equations
  3. Hamilton--Jacobi equations
  4. semiconvexity
  5. nondominated sorting
  6. applied probability

MSC codes

  1. 35D40
  2. 60F15
  3. 60C05

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Information & Authors

Information

Published In

cover image SIAM Journal on Mathematical Analysis
SIAM Journal on Mathematical Analysis
Pages: 872 - 911
ISSN (online): 1095-7154

History

Submitted: 11 August 2020
Accepted: 7 September 2021
Published online: 7 February 2022

Keywords

  1. viscosity solutions
  2. partial differential equations
  3. Hamilton--Jacobi equations
  4. semiconvexity
  5. nondominated sorting
  6. applied probability

MSC codes

  1. 35D40
  2. 60F15
  3. 60C05

Authors

Affiliations

Funding Information

National Science Foundation https://doi.org/10.13039/100000001 : DMS-1713691
University of Minnesota https://doi.org/10.13039/100007249

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