R^n空间中几乎凸不等式系统的全局误差界  

Global Error Bounds for Almost Convex Inequality System in R^n

作　　者：李军[1] 陈慧敏 LI Jun;CHEN Huimin(School of Mathematics and Information,China West Normal University,Nanchong Sichuan 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

出　　处：《西华师范大学学报（自然科学版）》2019年第1期1-6,共6页Journal of China West Normal University(Natural Sciences)

基　　金：国家自然科学基金项目(11871059;11371015);四川省高校创新团队(16TD0019);西华师范大学英才基金项目(17YC379)

摘　　要：全局误差界在数学规划问题的灵敏度分析以及各类算法的收敛性分析方面有重要应用。本文考虑有限维Euclidean空间中几乎凸不等式系统的全局误差界。通过利用Li和Mastroeni(见文献[13])研究的几乎凸集和几乎凸函数性质,借助于Deng(见文献[11])证明的误差界结果方法,证明了有限维Euclidean空间中几乎凸不等式系统全局误差界的存在性。Global error bounds have found important applications in sensitivity analysis of mathematical programming problems and convergence analysis of various algorithms.This paper investigates global error bounds for almost convex inequality system in finite dimensional Euclidean spaces.Employing the similar approach of Deng s error bounds result(see refference[13]),the existence of global error bounds of almost convex inequality system in finite dimensional Euclidean spaces is proved by the properties of almost convex sets and almost convex functions presented by Li and Mastroeni(see refference[11]).

关 键 词：几乎凸集 几乎凸函数 不等式系统 全局误差界 

分 类 号：O221[理学—运筹学与控制论]