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

Manifold Stratification Posit Dition Dinates 

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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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