Timeline for Faces of the intersection of convex sets
Current License: CC BY-SA 3.0
3 events
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| Nov 11, 2017 at 17:15 | comment | added | Guillaume | Indeed Denis Serre is referring to exposed faces, while the question was about faces, which is a more general definition. More about these two notions with examples/counterexamples can be found in Convex Analysis and Minimization Algorithms I, by J.B. Hirriart-Hurruty and C. Lemaréchal. | |
| Oct 31, 2017 at 14:10 | comment | added | Janko Bracic | I have upvoted the answer. It seems that the reasoning is correct at least for some faces. However it is not clear to me, why a face of $K$ is an intersection of $K$ and a supporting hyperplane. It seems to me that faces with this property are exposed faces. What if $F$ is a face of $K$ which is not exposed? | |
| Oct 30, 2017 at 19:09 | history | answered | Denis Serre | CC BY-SA 3.0 |