Optimization ( IF 2.2 ) Pub Date : 2021-04-01 , DOI: 10.1080/02331934.2021.1906873 Zhou Wei 1 , Jen-Chih Yao 2
In this paper, we mainly study applications of the calmness moduli for multifunctions to error bounds of several non-convex systems. Based on the work given in Shen et al. [Calmness and the Abadie CQ for multifunctions and linear regularity for a collection of closed sets. SIAM J Optim. 2019;29(3):2291–2319], we use results on the calmness modulus of the multifunction therein to study error bounds of differentiable inclusions, weak sharp minima of a lower semicontinuous function and linear regularity of finitely many closed subsets. Several primal equivalent conditions for these regularity properties of the corresponding non-convex systems are provided with some mild assumptions.
中文翻译:
函数的平静模量在误差范围内的应用
在本文中,我们主要研究了函数的平静模在几个非凸系统的误差界中的应用。基于 Shen 等人的工作。[Calmness 和 Abadie CQ 用于闭集集合的多功能和线性规律性。暹罗 J 优化。2019;29(3):2291-2319],我们使用其中的多功能平静模数的结果来研究可微夹杂物的误差界限、下半连续函数的弱锐最小值和有限多个封闭子集的线性规律。相应的非凸系统的这些规律性性质的几个原始等价条件被提供了一些温和的假设。