R^n空间中几乎凸不等式系统的度量正则性与全局误差界

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

误差界和度量正则性的研究在数学规划中起着非常重要的作用.本文考虑有限维Euclidean空间中几乎凸不等式系统的度量正则性、全局误差界与Slater条件之间的关系.通过利用Li和Mastroeni(见文献[8])研究的几乎凸集和几乎凸函数性质,借助于Deng(见文献[4])证明的度量正则性、全局误差界和Slater条件之间关系的结果方法,证明了有限维Euclidean空间中几乎凸不等式系统的度量正则性、全局误差界与Slater条件之间的关系.

It is well known that global error bounds and metric regularity play an important role in mathematical programming.This paper investigates the relationship among metric regularity,global error bounds and Slater conditions for almost convex inequality system in finite dimensional Euclidean spaces.Employing the similar approach of Deng’s results on metric regularity,global error bounds and Slater conditions(see[4]),the relationship among metric regularity,global error bounds and Slater conditions of almost convex inequality system in finite dimensional Euclidean spaces are proved by the properties of almost convex sets and almost convex functions obtained by Li and Mastroeni(see[8]).