ON THE CLARKE SUBDIFFERENTIAL OF THE DISTANCE FUNCTION OF A CLOSED SET

被引：66

作者：

BURKE, JV ^{[1
]}

FERRIS, MC ^{[1
]}

QIAN, MJ ^{[1
]}

机构：

[1] UNIV WISCONSIN,DEPT COMP SCI,MADISON,WI 53706

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 1992年 / 166卷 / 01期

关键词：

D O I：

10.1016/0022-247X(92)90336-C

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let C be a nonempty closed subset of the real normed linear space X. In this paper we determine the extent to which formulas for the Clarke subdifferential of the distance for C, dc(x) := inf y∈c {norm of matrix}x - y{norm of matrix}, which are valid when C is convex, remain valid when C is not convex. The assumption of subdifferential regularity for dc plays an important role. When x ∉ C, the most precise results also require the nonemptiness of the set PC(x) := { x ̄ ε{lunate} C : ∥x - x ̄∥ = dC(x)}. As an interesting side result, the equivalence between the strict differentiability and the regularity of dC at x is established when x ∉ C, PC(x) ≠ Ø, and the norm on X is smooth. © 1992.

引用

页码：199 / 213

页数：15

共 10 条

[1] THE DIFFERENTIABILITY OF REAL FUNCTIONS ON NORMED LINEAR-SPACE USING GENERALIZED SUBGRADIENTS [J].