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Date: 27-6-2021
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Date: 20-7-2021
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Date: 12-8-2021
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Given a subset and a point
, the contingent cone
at
with respect to
is defined to be the set
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where is the upper left Dini derivative of the distance function
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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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