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Date: 15-6-2021
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Given a subset and a point , the contingent cone at with respect to is defined to be the set
where is the upper left Dini derivative of the distance function
A classical result in convex analysis characterizes as the collection of vectors in for which there are sequences in and in such that lies in for all (Borwein). Intuitively, then, the contingent cone consists of limits of directions to points near in .
REFERENCES:
Borwein, J. and Lewis, A. Convex Analysis and Nonlinear Optimization: Theory and Examples. New York: Springer Science+Business Media, 2006.
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