c**a
发帖数: 316 | 1 Let K* the dual cone of a set K, i.e.
K* = {y|x'y >=0, for x in K}
Then text book states K** is the closure of the convex hull of K.
Consider K={x| ||x|| <= 1}.
Then we have K* = {0}, K** = R^n.
K** != K.
Where am I wrong?
Also,
If K = {x | a'x <= b}, and let a= [1,1], b =1.
Then K*= {0} as well and K** = R^2.
K** != K. | Q***5
发帖数: 994 | 2 Are you sure it is "convex hull", not "conic hull"?
【在 c**a 的大作中提到】
: Let K* the dual cone of a set K, i.e.
: K* = {y|x'y >=0, for x in K}
: Then text book states K** is the closure of the convex hull of K.
: Consider K={x| ||x|| <= 1}.
: Then we have K* = {0}, K** = R^n.
: K** != K.
: Where am I wrong?
: Also,
: If K = {x | a'x <= b}, and let a= [1,1], b =1.
: Then K*= {0} as well and K** = R^2.
| c**a
发帖数: 316 | 3 "Convex Optimization" By Stephen Boyd, Cambridge Press, Seventh printing
with corrections, 2009, p. 53. | c**a
发帖数: 316 | 4 "Convex Optimization" By Stephen Boyd, Cambridge Press, Seventh printing
with corrections, 2009, p. 53. | c**a
发帖数: 316 | 5 Dual cones satisfy several properties, such as:
* ...
* ...
* ...
* ...
* K** is the closure of the convex hull of K. (Hence, if K is convex and
closed, K** = K).
The content in the parenthesis was by the original authors, i.e. Boyd. | Q***5
发帖数: 994 | 6 那里，K本身是 cone。你举的例子K只是convex,不是 cone. | c**a
发帖数: 316 | | c**a
发帖数: 316 | 8 First sentence of section 2.6.1.
Let K be a cone.... |
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