# 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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### what is a variational form in optimization?

This is probably a pretty basic question, but I can't figure out what people mean when they say "variational forms" in optimization. For example, in this paper I'm reading, the variational form of a ...
173 views

### 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 ...
413 views

### Finding extremal 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. ...
107 views

### 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. ...
741 views

### What are prerequisites to Terry Tao's An Introduction To Measure Theory?

I am an economics student and want to study mathematics, variational analysis in particular, with measure approach but since I am ignorant of measure theory I decided to try this book but I still find ...
306 views

### Looking for a rigorous treatment of the functional derivative the way it's used by physicists.

A lot of theories in physics can be derived from a variational principle: some action functional S on a space of e.g. field configurations $\phi$ is given, and the equations of the theory follow from ...
88 views

121 views

### All the symmetries of the Dirichlet energy are conformal

It seems to be "folklore" knowledge that all the (source) symmetries of the $d$-Dirichlet energy are conformal maps. Specifically, I have found this nice proof for the following claim: Proposition:...
112 views

### The integral under the variation $\delta$ sign
In physics books on classical field theory, the authors usually define the action as $$S = \int\mathcal{L(\phi,\partial_\mu\phi)d^4x}$$ where $\mathcal{L}$ is the lagrangian density. Then, ...