# Questions tagged [variational-analysis]

Variational analysis is a branch of mathematics that extends the methods arising from the classic calculus of variations and convex analysis to more general problems of optimization theory, including topics in set-valued analysis, e.g. generalized derivatives.

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### Finding stationary point of the functional

Find the stationary point of the functional $$J[y]=\int \left( x^2y'^2+2y^2 \right) dx$$ where $y(0)=0, y(1)=2.$ My Solution: E-L equation: $x^2y''+2xy'-2y=0.$ This is also Cauchy-Euler equation. ...
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### Reparameterization Trick in VAE

I was reading on variational auto-encoders https://wiseodd.github.io/techblog/2016/12/10/variational-autoencoder/ and am unable to understand how the function below is generated. Based on my limited ...
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### Convert differential equation to variational statement

I know how to convert a differential equation with constant coefficients to variational form. But the question in the picture has non-constant coefficients. How do people get around that? Any ...
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### (Stochastic Variational inference) What is the expectation of natural parameter with respect to approximate density?

Apologize if this is a stupid question. I am working with Stochastic Variational inference of regression having both local hidden variable (z) and global hidden variable ($\beta$), and $x$ is the ...
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### Understanding a variational calculus argument in the Hamiltonian setting

On pg. 102 of No-Nonsense Classical Mechanics, the author assumes that $S$ is a minimum so that when we add $\epsilon$ to $q$ and $\tilde{\epsilon}$ to $p$, we obtain that $S$ is equal to which ...
Let $D$ be a closed nonempty set in $\mathbb{R}^{m}$. Let $f: \mathbb{R}^{m} \times (0, \infty) \to \overline{\mathbb{R}}$ be a lower semicontinuous function such that $f(u, r) \nearrow \delta_{D}(u)$ ...