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.

164 questions
Filter by
Sorted by
Tagged with
18 views

The minima of a function depends of the norm [closed]

I need help to prove the next statement. Thank you.
40 views

Euler Lagrange equation in variational calculus for a sum of integrals

Let $F, G: \mathbb{R}^3\rightarrow{}\mathbb{R}$ be two continuously differentiable functions and let $a\leq b \leq c$. I want to know if there exists some known method to find a function that ...
21 views

Extending the domain of a lower semicontinuous function

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 $f(u, r) \nearrow \delta_{D}(u)$ ...
24 views

What constraints can be imposed to a variational problem to render a surface with a given curvature?

The problem was motivated by the following situation: Suppose we had a grinding device like the mortar with pestle as shown in the following picture The pictured pestle may suggest a surface with ...
6 views

22 views

63 views

What is $\max\langle x,Ax\rangle$ over subspaces non-invariant under $A$?

Let $A$ be an Hermitian matrix in a vector space $V$, and let $U\le V$ be a subspace of $V$. If $U$ is invariant under $A$, then the maximum of $\langle x,Ax\rangle$ over all unit vectors $x\in U$ ...