水平函数的存在性(英文)

Existence on Level Functions of a Function

证明拓扑向量空间上的连续拟凸函数在任何点处的水平函数集非空,得到水平函数的次微分与函数水平集的法向锥之关系,利用水平函数集给出函数存在最小值点的一个充分条件,刻画了某些水平函数的特征。

we proposed a level function of a function at a point and studied its existence, presenting the result that set of level functions for continuous quasiconvex function at any point is nonempty. The relations between subdifferential of level functions and normal cone of level set are described and a sufficient condition for exis tence of minimal point of a function is shown. Characteristics of some level functions are derived.