Structure of approximate solutions of variational problems
with extended-valued convex
integrands

Alexander J. Zaslavski

Displaying similar documents to “Structure of approximate solutions of variational problems with extended-valued convex integrands”

Generalized Characterization of the Convex Envelope of a Function

Fethi Kadhi (2010)

RAIRO - Operations Research

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We investigate the minima of functionals of the form $\int_{[a, b]} g (\dot{u} (s)) d s$ where is strictly convex. The admissible functions $u : [a, b] ⟶ ℝ$ are not necessarily convex and satisfy $u \leq f$ on , , , is a fixed function on . We show that the minimum is attained by $\bar{f}$ , the convex envelope of .

An improved derandomized approximation algorithm for the max-controlled set problem

Carlos Martinhon, Fábio Protti (2011)

RAIRO - Theoretical Informatics and Applications

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A vertex of a graph = () is said to be by $M \subseteq V$ if the majority of the elements of the neighborhood of (including itself) belong to . The set is a in if every vertex $i \in V$ is controlled by . Given a set $M \subseteq V$ and two graphs = ( $V, E_{1}$ ) and = ( $V, E_{2}$ ) where $E_{1} \subseteq E_{2}$ , the consists of deciding whether there exists a sandwich graph = () (, a graph where $E_{1} \subseteq E \subseteq E_{2}$ ) such that is a monopoly in = (). If the answer to the is No, we then consider the , whose objective is to find a sandwich...

An improved derandomized approximation algorithm for the max-controlled set problem

Carlos Martinhon, Fábio Protti (2011)

RAIRO - Theoretical Informatics and Applications

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On the asymptotic properties of a simple estimate of the Mode

Christophe Abraham, Gérard Biau, Benoît Cadre (2010)

ESAIM: Probability and Statistics

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We consider an estimate of the mode of a multivariate probability density with support in $ℝ^{d}$ using a kernel estimate drawn from a sample . The estimate is defined as any in {} such that $f_{n} (x) = {max}_{i = 1, \dots, n} f_{n} (X_{i})$ . It is shown that behaves asymptotically as any maximizer ${\hat{θ}}_{n}$ of . More precisely, we prove that for any sequence ${(r_{n})}_{n \geq 1}$ of positive real numbers such that $r_{n} \to \infty$ and $r_{n}^{d} log n / n \to 0$ , one has $r_{n} ∥ θ_{n} - {\hat{θ}}_{n} ∥ \to 0$ in probability. The asymptotic normality of follows without further work.