论文标题
非主导分类的连续限制的收敛速率
Rates of convergence for the continuum limit of nondominated sorting
论文作者
论文摘要
非主导排序是一个离散的过程，根据坐标部分阶订单将点在欧几里得空间中分类，用于对可行解决方案进行多目标优化问题进行排名。以前显示，随机点的非主导分选具有汉密尔顿 - 雅各布方程连续性极限。我们证明了非主导排序与其连续性限制汉密尔顿 - 雅各比方程的收敛性的定量误差估计。我们的证明使用了最大原理和粘度解决方案机制，以及具有角落奇点的域的新半蔬菜估计。
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.
