Strictly Quasi-Convex Sets
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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!