一类非凸多面体集合上的切锥表达式研究

Study on the Expression of Tangent Cone on a Class of Nonconvex Polyhedron Sets

切锥是变分分析中的一个重要概念,它的应用十分广泛。本文首先通过正则法锥、法锥、切锥和极锥的概念和性质,建立了一类非凸多面体集合的切锥表达式。然后通过切锥与内切锥的关系,证明了这类非凸多面体集合的切锥和内切锥的等价性。最后将这个结果应用到集值映射的广义可微性中,展现了这个等价性的重要意义。

Tangent cone is an important concept in variational analysis, which is widely used. In this paper, firstly, through the concepts and properties of regular normal cone, normal cone, tangent cone and polar cone, the tangent cone expression of a class of nonconvex polyhedron sets is established. Then, through the relationship between tangent cone and innertangent cone, the equivalence of tangent cone and innertangent cone of this kind of nonconvex polyhedron sets is proved. Finally, this result is applied to the generalized differentiability of set-valued mapping, which shows the significance of this equivalence.