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Properties of Derivates and Some Applications

In: Variational Analysis and Generalized Differentiation in Optimization and Control

Author

Listed:
  • Michael McAsey

    (Bradley University)

  • Libin Mou

    (Bradley University)

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.

Suggested Citation

  • Michael McAsey & Libin Mou, 2010. "Properties of Derivates and Some Applications," Springer Optimization and Its Applications, in: Regina S. Burachik & Jen-Chih Yao (ed.), Variational Analysis and Generalized Differentiation in Optimization and Control, pages 43-57, Springer.
    • Handle: RePEc:spr:spochp:978-1-4419-0437-9_2
    DOI: 10.1007/978-1-4419-0437-9_2
    as

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