  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.
