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Strictly Quasi-Convex Sets

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

Abstract

The quasi-convex sets introduced in  Chap. 6 do a good job in generalizing the properties of convex sets with respect to uniqueness, stability, and existence of the projection. But they miss their point on the subject of parasitic stationary points. So we shall start in this chapter from a complementary point of view, and introduce in Sect. 7.1 another family of sets, called the strictly quasi-convex sets (s.q.c. sets in short) which, almost by definition, will ensure the absence of parasitic stationary points. Note that the name “s.q.c.” has provisorily to be taken as a whole, as it will not be clear at all from the definition that s.q.c. sets are quasi-convex!

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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