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Limiting behavior of the approximate second-order subdifferential of a convex function. (English) Zbl 0792.49015
Summary: J.-B. Hiriart-Urruty and the author [Proc. Lond. Math. Soc., III. Ser. 58, No. 2, 351-365 (1989; Zbl 0663.53006)] recently introduced the notions of Dupin indicatrices for nonsmooth convex surfaces and studied them in connection with their concept of a second-order subdifferential for convex functions. They noticed that second-order subdifferentials can be viewed as limit sets of difference quotients involving approximate subdifferentials. In this paper, we elaborate this point in a more detailed way and discuss some related questions.

MSC:
49J52 Nonsmooth analysis
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