Regularity of set-valued maps and their selections through set differences. Part 1: Lipschitz continuity

Robert Baier; Elza Farkhi

Journal articles

Regularity of set-valued maps and their selections through set differences. Part 1: Lipschitz continuity

Robert Baier ¹ Elza Farkhi ²

2 School of Mathematical Sciences [Tel Aviv]

Abstract : We introduce Lipschitz continuity of set-valued maps with respect to a given set di erence. The existence of Lipschitz selections that pass through any point of the graph of the map and inherit its Lipschitz constant is studied. We show that the Lipschitz property of the set-valued map with respect to the Demyanov di erence with a given constant is characterized by the same property of its generalized Steiner selections. For a univariate multifunction with only compact values in Rn, we characterize its Lipschitz continuity in the Hausdor metric (with respect to the metric di erence) by the same property of its metric selections with the same constant.

Document type :

Journal articles

Domain :

Mathematics [math] / Optimization and Control [math.OC]

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https://hal.inria.fr/hal-01067206
Contributor : Estelle Bouzat Connect in order to contact the contributor
Submitted on : Tuesday, September 23, 2014 - 11:03:20 AM
Last modification on : Friday, October 13, 2017 - 5:08:16 PM

Regularity of set-valued maps and their selections through set differences. Part 1: Lipschitz continuity

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Regularity of set-valued maps and their selections through set differences. Part 1: Lipschitz continuity

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