Properties of Derivates and Some Applications

Michael McAsey () and Libin Mou ()
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Michael McAsey: Bradley University
Libin Mou: Bradley University

A chapter in Variational Analysis and Generalized Differentiation in Optimization and Control, 2010, pp 43-57 from Springer

Abstract: Abstract In this chapter, we generalize the concept of derivates, defined recently in the literature, to maps defined on a topological space. The derivate of a map has some interesting properties and applications to optimization problems. For example, it is closely related to various notions of tangent spaces of the range of the map. It strengthens the necessary condition (Fermat’s theorem) for an extremum point to a sufficient condition.

Keywords: Banach Space; Topological Space; Chain Rule; Smooth Banach Space; Local Minimum Point (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4419-0437-9_2

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DOI: 10.1007/978-1-4419-0437-9_2

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