# 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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### An $\mathcal{L}^1$ optimization problem in function space

Let $f: (-\infty,\infty)\to [0,\infty)$ be a smooth map. Then, how to solve the following optimizatin problem w.r.t. $f$? \begin{align} \mathrm{minimize}_f&~~\int_{-\infty}^{\infty} |f(x) - \exp(-...
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### 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, ...
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I need some help with the development of an expression, it is: $$\delta\left\{\frac{\partial^3F(q^1,q^2,t)}{\partial t\partial q^1 \partial q^2}\right\}$$ with each of $q^1,q^2$ are functions of $t$. ...
Could you please help to me to compute the following $\epsilon$-normal set: Given $\epsilon>0$, how to compute the $\epsilon$-normal set of $C:=[2,\infty)\times \Bbb{R}$ at the point $(2,0)$. Thank ...
### $\epsilon$-normals to convex sets
I am reading the book by B. Mordukhovich, Variational analysis and generalized differentiation I. On page 6 it is stated the following inclusion:  \hat{N}_{\varepsilon }\left( \bar{x};\Omega \right)...