一类Minkowski泛函的若干性质

Some properties of Minkowski functionals in Linear spaces

研究一类特殊的Minkowski泛函—PA(x)。基于该函数在凸性条件下的基本性质,研究了它在仿凸集下的若干性质。首先回答了文献[1]中的公开问题,并给出了证明。其次,研究了在全空间下PA(x)和凸锥下PA(x)的特殊性质。最后,利用凸函数的次微分定义给出了PA(x)的次微分的计算结果。

In this paper,we use the definition of Minkowski functional and the basic properties under convex conditions to further study the generalized properties under the pseudo-convex set.First,the key issues in the literature[1]are addressed,and specific examples are given.In particular,the properties and results of Minkowski functionals and Minkowski functionals under convex cones in full space are studied.Finally,the subdifferential of Minkowski functional is studied by the subdifferential definition of convex function.