Demyanov difference in infinite-dimensional spaces. (English) Zbl 1281.49008

Demyanov, Vladimir F. (ed.) et al., Constructive nonsmooth analysis and related topics. New York, NY: Springer (ISBN 978-1-4614-8614-5/hbk; 978-1-4614-8615-2/ebook). Springer Optimization and Its Applications 87, 13-24 (2014).
Summary: In this paper, we generalize the Demyanov difference to the case of real Hausdorff topological vector spaces. We prove some classical properties of the Demyanov difference. In the proofs, we use a new technique which is based on the properties given in Lemma 1. Due to its importance it will be called the preparation lemma. Moreover, we give connections between Minkowski subtraction and the union of upper differences. We show that in the case of normed spaces the Demyanov difference coincides with classical definitions of Demyanov subtraction.
For the entire collection see [Zbl 1278.49002].


49J52 Nonsmooth analysis
49N15 Duality theory (optimization)
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