Difference between revisions of "Talk:Subdifferential"
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: Could you please explain a little, what is the problem? I do not have that book on my table. I also note that compactness is required. --[[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 23:22, 7 October 2013 (CEST) | : Could you please explain a little, what is the problem? I do not have that book on my table. I also note that compactness is required. --[[User:Boris Tsirelson|Boris Tsirelson]] ([[User talk:Boris Tsirelson|talk]]) 23:22, 7 October 2013 (CEST) | ||
| − | ::This is a corollary of Theorem 23.5 that relates the subdifferential of a convex function to its dual function. It says | + | ::This is a corollary 23.5.3 of Theorem 23.5 that relates the subdifferential of a convex function to its dual function. It says |
::''Let C be a non empty closed convex set. Then for h the support function of C and each vector x, the subdifferential of h at x consists of the points (if any) where the linear function <.,x> achieves its maximum over C.'' | ::''Let C be a non empty closed convex set. Then for h the support function of C and each vector x, the subdifferential of h at x consists of the points (if any) where the linear function <.,x> achieves its maximum over C.'' | ||
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| + | ::To me this does not agree with the claim about the subdifferential of the support function of a compact subset. | ||
Revision as of 12:00, 8 October 2013
The article says
"The subdifferential of the support function of a convex set coincides with the set itself"
This seems to disagree with corollary 25.5.3 of Rockafellar's book. Or am I mistaken?
- Could you please explain a little, what is the problem? I do not have that book on my table. I also note that compactness is required. --Boris Tsirelson (talk) 23:22, 7 October 2013 (CEST)
- This is a corollary 23.5.3 of Theorem 23.5 that relates the subdifferential of a convex function to its dual function. It says
- Let C be a non empty closed convex set. Then for h the support function of C and each vector x, the subdifferential of h at x consists of the points (if any) where the linear function <.,x> achieves its maximum over C.
- To me this does not agree with the claim about the subdifferential of the support function of a compact subset.
How to Cite This Entry:
Subdifferential. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Subdifferential&oldid=30605
Subdifferential. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Subdifferential&oldid=30605