# Questions tagged [variational-inequalities]

The variational-inequalities tag has no usage guidance.

The variational-inequalities tag has no usage guidance.

9
questions

0
votes

1
answer

56
views

Let $X$ be a reflexive Banach space, $z, x, v \in X$. $\{z_i\}, \{x_i\}$ and $\{v_i\}$ are arbitrary sequences converging to $z, x$ and $v$, respectively.
I would like to know under which conditions ...

1
vote

1
answer

90
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Let $X$ be a reflexive Banach space, $z, x, v \in X$. If $f: X \times X \rightarrow \mathbb{R}$ is continuous regarding its first argument and locally Lipschitz regarding its second argument. $\{z_i\},...

2
votes

1
answer

93
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Why is the Ekeland variational theorem called the Ekeland variational principle?
I think (or maybe I studied somewhere) this is because of its equivalency with the Takahashi theorem, the Caristi ...

2
votes

1
answer

172
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$\DeclareMathOperator\Ent{Ent}\newcommand{\prior}{\mathrm{prior}}\newcommand\Data{\mathrm{Data}}$I came across this paper on the optimality of Bayes' theorem
https://sinews.siam.org/Portals/Sinews2/...

3
votes

1
answer

203
views

I have an optimization problem with a variational inequality constraint:
$$
\begin{equation}
\begin{array}{ll}
\min_x & f(x) \\
\mathrm{s.t.} & g_i(x) \leq 0, \quad i=1,\ldots,m \\
& h_j(...

2
votes

0
answers

117
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When reading some old notes of my advisor on interpolation spaces, I bumped into a problem I can't quite wrap my head around. Here are the details.
For $p\in(0,\infty)$ a $p$-variation semi-norm of a ...

4
votes

1
answer

461
views

I want to find a bound for the operator norm of the Fréchet derivative of a Lipschitz continuous function in the following setting:
Let
$E$ be a $\mathbb R$-Banach space;
$v:E\to[1,\infty)$ be ...

2
votes

1
answer

95
views

Consider the free boundary problem
$$
\min\{u_t - u_{xx} -1, u \} = 0 \qquad \text{ in } (0,T)\times (-1,1) \\
u(0,\cdot) = 0 \qquad \text{ in } (-1,1)\\
u(\cdot, -1) = u(\cdot, 1) = 0 \qquad \...

2
votes

1
answer

171
views

I want to solve a parabolic obstacle problem, written as a variational inequality: For almost all $t\in [0,T]$
\begin{align*}
\langle u'(t), v - u(t)\rangle +a(u(t),v-u(t)) \geq \langle f(t),v-u(t)\...