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Zbl 0886.49018
Huang, L.R.; Ng, K.F.
On lower bounds of the second-order directional derivatives of Ben-Tal, Zowe, and Chaney. (English)
[J] Math. Oper. Res. 22, No.3, 747-753 (1997). ISSN 1526-5471; ISSN 0364-765X/e

This authors studied the generalized second-order directional derivative of Demyanov-Pevnyi and Ben-Tal-Zowe type. It was shown that upper and lower second-order directional derivatives have the same lower bound for a fixed unit direction. These results were used to characterize the convexity of a real-valued function.
[X.Q.Yang (Nedlands)]

MSC 2000:: *49J52 Nonsmooth analysis (other weak concepts of optimality)
90C25 Convex programming

Keywords: second-order directional derivative; Lipschitz function

Cited in: Zbl 1040.49024

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