# Questions tagged [variational-inequalities]

The tag has no usage guidance.

6 questions
Filter by
Sorted by
Tagged with
108 views

### An inequality in the optimality of Bayes' theorem

$\DeclareMathOperator\Ent{Ent}\newcommand{\prior}{\mathrm{prior}}\newcommand\Data{\mathrm{Data}}$I came across this paper on the optimality of Bayes' theorem https://sinews.siam.org/Portals/Sinews2/...
I have an optimization problem with a variational inequality constraint: $$\begin{equation} \begin{array}{ll} \min_x & f(x) \\ \mathrm{s.t.} & g_i(x) \leq 0, \quad i=1,\ldots,m \\ & h_j(... 0answers 105 views ### Estimate involving Besov norm When reading some old notes of my advisor on interpolation spaces, I bumped into a problem I can't quite wrap my head around. Here are the details. For p\in(0,\infty) a p-variation semi-norm of a ... 1answer 247 views ### Bound the operator norm of the Fréchet derivative of a Lipschitz function in this setting I want to find a bound for the operator norm of the Fréchet derivative of a Lipschitz continuous function in the following setting: Let E be a \mathbb R-Banach space; v:E\to[1,\infty) be ... 1answer 86 views ### Explicit solution of a free boundary problem for heat equation Consider the free boundary problem$$ \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 \...
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)\...