Abstract
In Chapter 2 we developed Morse Theory for functions which are defined on the whole ℝn. In this chapter we study Morse Theory for functions which need not to be defined on the whole ℝn 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 ℝn.
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© 2001 Springer Science+Business Media Dordrecht
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Jongen, H.T., Jonker, P., Twilt, F. (2001). Morse theory (with constraints). In: Nonlinear Optimization in Finite Dimensions. Nonconvex Optimization and Its Applications, vol 47. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0017-9_3
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DOI: https://doi.org/10.1007/978-1-4615-0017-9_3
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-4887-0
Online ISBN: 978-1-4615-0017-9
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