【摘要】 用函数的上图象之间的Hausdorff距离定义向量值函数间的距离,在此弱拓扑下研究了定义在紧距离空间上的一类具有普遍意义的n维向量值函数弱有效解的稳定性,指出在Baire分类意义下,大多数这类向量值函数的弱有效解是稳定的,且任一n维向量值函数都可以用所谓的本质函数来逼近。更多还原

【Abstract】 The distance between two functionals is defined by the Hausdorff distance between the epigraphs of the two functionals. In this weak topology case, we research the stability of the weakly efficient solutions of a kind of general meanings n-dimensioned vector-valued functionals. As results, we point out that, from the viewpoint of Baire’s category, most of the vector optimization problems have stable weakly efficient solutions and that any this kind of function can be arbitrarily approximated by a sequence of so-called essential vector-valued functionals.更多还原