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Seeger, A.

Limiting behavior of the approximate second-order subdifferential of a convex function. (English) Zbl 0792.49015

J. Optimization Theory Appl. 74, No. 3, 527-544 (1992).
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.

Cited in 5 Documents

MSC:

49J52 Nonsmooth analysis

Keywords:

approximate subdifferential; second-order subdifferential; Legendre- Fenchel transform; epiconvergence; Dupin indicatrices; nonsmooth convex surfaces

Citations:

Zbl 0663.53006
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\textit{A. Seeger}, J. Optim. Theory Appl. 74, No. 3, 527--544 (1992; Zbl 0792.49015)
Full Text: DOI

References:

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