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Results tagged with calculus-of-variations
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user 32507
Questions on the calculus of variations, which deals with the optimization of functionals mostly defined on infinite dimensional spaces.
1
vote
Optimal transport: how $\varphi^c$ can be written as $\varphi^c = \lim _{\ell \rightarrow \i...
Here is an example which shows that also the continuity of $\varphi$ does not help. Let $X = \mathbb R$ and $Y = \{0\}$. In the sequel, we will just drop the $Y$-argument. Let $c \equiv 1$, $\varphi \ …
- 1,724
8
votes
What are the major differences between real and complex Banach space?
In optimization, you typically have a function $f \colon X \to \mathbb{R}$ which you are going to minimize. In order to apply first-order optimality conditions or first-order methods, you would like t …
- 1,724
1
vote
Optimal transport: the existence of an optimal pair of $c$-conjugate functions
I was also struggling with Exercise 2.36... I think that I am now able to solve it, although it seems that it is more difficult than it appears...
The key seems to be the following theorem.
Theorem: …
- 1,724