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.

Filter by
Sorted by
Tagged with
0
votes
1answer
85 views

Difficulty Understanding Sufficient Conditions for Weak Extrema in Calculus of Variations

I am having a difficult time understanding Jacobi's necessary condition for weak extrema of functionals. Graphics and detailed explanations would be helpful. I am following the following two texts: ...
3
votes
1answer
82 views

Characterisation of the rate distortion function: issue with functional derivative

In Elements of Information Theory, I can't figure out how the functional derivative $ \frac{\delta J}{\delta q(\hat{x}|x)} $ for $ J(q) = \sum_x \sum_{\hat{x}} p(x)q(\hat{x}|x)\log{\frac{q(\hat{x}|x)}{...
2
votes
1answer
236 views

$\epsilon$-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)...
2
votes
2answers
318 views

Permutation and combinations using chairs?

After reading and watching a lot about permutation, combination and variation i still don't understand them fully. So i have two questions: How many ways are there to position 5 people on 10 chairs? ...
2
votes
3answers
137 views

Euler-Lagrange formula

Let $y:[-1,1]\to [2-1,2+1]$ be a $C^1$-smooth function, and $F(y,y'):=y\sqrt{1+y'^2}$. Suppose $y(x)$ satisfy the Euler-Lagrange equation, i.e. $$\frac{\partial F}{\partial y}-\frac{d}{dx}\frac{\...
0
votes
2answers
67 views

Calculus of Variations (Gelfand & Fomin): Proof of Euler's Equation for Constrained Variation

I am in Section 2.12.1 of Calculus of Variations by Gelfand & Fomin. I am attempting to follow the proof of the Euler equation for Constrained Variation (Theorem 1, pg. 42). However, I'm confused ...