凸集的强锥包相交性与上图和正则条件(英文)

Strong CHIP of convex sets and epi-sum regularity

在局部凸拓扑向量空间上讨论凸集的上图和正则条件与强锥包相交性之间的关系。首先将上图和正则条件能蕴含强锥包相交性的结果从Banach空间推广到局部凸拓扑向量空间上,然后引入简单渐近集的概念,并且证明出当凸集之交是一个简单渐近集(包括有界集、凸集、仿射集)时,强锥包相交性能够蕴含强锥包相交性。

The relationship between the epi-sum regularity condition convex spaces is discussed. First, the result that the epi - sum regulari and the strong CHIP in locally ty condition implies the strong CHIP is explored from Banach space into locally convex spaces; and then, the concept of simple asymptotical set is introduced, and it is proved that the converse is true in some special cases when the intersection of convex sets is a simple asymptotical set, which includes bounded sets, convex cones, and affine sets.