All Questions
Tagged with functional-calculus calculus-of-variations
8 questions
2
votes
1
answer
427
views
How to solve an optimization problem whose optimization variable is a function?
I would like to find an optimal probability density function (PDF) $f$. Given $b$,
$$ \begin{array}{ll} \underset {f} {\text{minimize}} & C \\ \text{subject to} & 1 + \frac{b}{x} \displaystyle\...
- 21
5
votes
0
answers
138
views
Functional inverse problem based on a variational principle
I am trying to solve an inverse problem based on variational principle.
I will first present a forward problem that is already solved, and then present the inverse problem that I am trying currently ...
2
votes
4
answers
337
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EM-wave equation in matter from Lagrangian
Note
I am not sure if this post is of relevance for this platform, but I already asked the question in Physics Stack Exchange and in Mathematics Stack Exchange without success.
Setup
Let's suppose a ...
- 61
3
votes
0
answers
203
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Gelfand "Calculus of Variation" 1.7 question on definition and purpose of variational derivative
In Gelfand Calculus of Variation, chapter 1.7, the variational derivative is defined as:
$$\left.\frac{\partial J}{\partial y}\right|_{x = x_0} = \lim_{\Delta\sigma \rightarrow 0}\frac{J[y+h]-J[y]}{\...
- 31
2
votes
1
answer
521
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Fréchet derivative of evaluation-like functional (multivariate)
I'm fairly new to functional calculus but and posting here since the question seems more appropriate than for MSE. When coming across this post I could not help but wonder the following.
Let $H$ be ...
- 5,405
1
vote
1
answer
246
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Variational problem: how to minimise the second moment?
This is a neater version of a question I posted here, on which I'm also stuck.
The problem: Say I have a probability density function $f(x)$, defined for positive $x$, and let's note its $n$th non-...
- 223
0
votes
1
answer
203
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Variation in Einstein-Hilbert action [closed]
In this page there are calculations of variation of Einstein-Hilbert action.
I see variations of terms like this:
$\delta {R^{\rho }}_{{\sigma \mu \nu }}$
where the term is not a functional, and ...
- 111
4
votes
1
answer
428
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Reference Request: Calculus of Variations in Hilbert Space
I'm looking for a good reference to a book on calculus of variations in the setting of Banach Spaces.
If it helps, I'm working with a particular functional acting on Fr\'{e}chet-differentiable ...
