奇异延拓：通过全局分析生成Pareto集的逐段线性逼近
Singular Continuation: Generating Piece-wise Linear Approximations to Pareto Sets via Global Analysis
摘要：
我们提出了一个战略，近似帕累托最优集的基础上提出的全球分析框架Smale（动力系统，纽约，1973年，第100页）。531-544）。该方法突出和利用帕累托集的基本流形结构，通过单纯复形近似帕累托最优解。该方法区分了奇异集、Pareto临界集和稳定Pareto临界集之间的层次关系，并能处理一般非凸情形下局部Pareto前沿的叠加问题.此外，一个平方收敛结果在一个合适的集明智的意义证明和测试的数值例子。
英文摘要：
We propose a strategy for approximating Pareto optimal sets based on the global analysis framework proposed by Smale (Dynamical systems, New York, 1973, pp. 531-544). The method highlights and exploits the underlying manifold structure of the Pareto sets, approximating Pareto optima by means of simplicial complexes. The method distinguishes the hierarchy between singular set, Pareto critical set and stable Pareto critical set, and can handle the problem of superposition of local Pareto fronts, occurring in the general nonconvex case. Furthermore, a quadratic convergence result in a suitable set-wise sense is proven and tested in a number of numerical examples.
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