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Quasi-Convex Sets

  • Guy ChaventEmail author
Chapter
  • 2k Downloads
Part of the Scientific Computation book series (SCIENTCOMP)

Abstract

In this chapter, we define a new class of subsets of a Hilbert space, called the quasi-convex sets to which properties (i) (uniqueness), (iii) (stability) and (iv) (existence as soon as the set is closed) of Proposition 4.1.1 can be generalized, provided they are required to hold only on some neighborhood. Technically, the whole chapter will consist in adapting the classical proofs for convex sets to the case where the segments are replaced by paths with finite curvature.

We postpone to Chap. 7 the generalization of property (ii) on the absence of parasitic stationary points.

Keywords

Cauchy Sequence Obtuse Angle Classical Proof Minimum Length Path Nonlinear Inverse Problem 
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.

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Ceremade, Université Paris-DauphineParis Cedex 16France
  2. 2.Inria-RocquencourtLe Chesnay CedexFrance

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