3 Tricks To Get More Eyeballs On Your Duality Theorem
Then extend
f
{\displaystyle {\tilde {f}}}
to a perturbation function
F
:
see post X
Y
R
{
+
}
{\displaystyle F:X\times Y\to \mathbb {R} \cup \{+\infty \}}
such that
F
(
x
,
0
)
=
(
x
)
{\displaystyle F(x,0)={\tilde {f}}(x)}
.
The three properties of the dual cone carry over to this type of duality by replacing subsets of
R
2
{\displaystyle \mathbb {R} ^{2}}
by vector space and inclusions of such subsets by linear maps. .