Set-valued differentiation as an operator

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dc.creatorSamborski, Serguei
dc.date2005-09-07
dc.date.accessioned2026-07-07T05:23:02Z
dc.date.available2026-07-07T05:23:02Z
dc.descriptionWe introduce real vector spaces composed of set-valued maps on an open set. They are also complete metric spaces, lattices, commutative rings. The set of differentiable functions is a dense subset of these spaces and the classical gradient may be extended in these spaces as a closed operator. If a function f belongs to the domain of such extension, then f is locally lipschitzian and the values of extended gradient coincide with the values of Clarke's gradient. However, unlike Clarke's gradient, our generalized gradient is a linear operator.
dc.identifierhttps://arxiv.org/abs/math/0509167
dc.identifierhttp://arxiv.org/abs/math/0509167
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76285
dc.subjectOptimization and Control
dc.subject49K99
dc.titleSet-valued differentiation as an operator
dc.typetext

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