Morse theory (with constraints)
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 .
KeywordsManifold Stratification Posit Dition Dinates
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