Abstract
The sticky face lemma describes the local behavior of the inverse of the normal-cone operator of a polyhedral convex set. This inverse, when applied to a vector, produces a face of the set. The lemma says that small perturbations of the vector produce only subfaces of the original face. This property is useful in analyzing variational analysis and optimization problems whose underlying sets are convex and polyhedral.
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This material is based on work supported by the Air Force Research Laboratory under awards FA9550-10-1-0101 and FA9550-15-1-0212. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author and do not necessarily reflect the views of the sponsoring agency.
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Robinson, S.M. A Short Proof of the Sticky Face Lemma. Math. Program. 168, 5–9 (2018). https://doi.org/10.1007/s10107-016-1037-z
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DOI: https://doi.org/10.1007/s10107-016-1037-z