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Morse theory (with constraints)

  • Hubertus Th. Jongen
  • Peter Jonker
  • Frank Twilt
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 47)

Abstract

In Chapter 2 we developed Morse Theory for functions which are defined on the whole ℝ n . In this chapter we study Morse Theory for functions which need not to be defined on the whole ℝ n but merely on suitable subsets of it: C r -manifolds (see Section 2.1) or, more generally, “C r -Manifolds with Generalized Boundary”. A very important subclass of the latter geometric object is formed by the so-called “Regular Constraint Sets” (especially in view of optimization theory). The aim of this section is to introduce such subsets of ℝ n .

Keywords

Vector Field Open Neighborhood Tangent Cone Morse Theory Relative Interior 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Hubertus Th. Jongen
    • 1
  • Peter Jonker
    • 2
  • Frank Twilt
    • 2
  1. 1.Department of MathematicsAachen University of TechnologyAachenGermany
  2. 2.Department of Mathematical SciencesUniversity of TwenteEnschedeThe Netherlands

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