Data di Pubblicazione:
2005
Citazione:
One-point location problems from a very general point of view / L. Vesely. - In: RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO. SUPPLEMENTO. - ISSN 1592-9531. - 76:(2005), pp. 635-653.
Abstract:
Given a nonempty set $A$ in a metric space $(X,d)$, we consider the
problem of minimizing a function $\phi\colon X\to\R$ of the form
\[
\phi(x)=f(\Delta_x)\,,
\]
where $f$ is a monotone functional on the set $\lip(A)$ of all nonnegative
$1$-Lipschitz functions on $A$, and $\Delta_x\colon A\to\R_+$ is the
($1$-Lipschitz) function $\Delta_x(\cdot)=d(x,\cdot)$.
The minimizers (if any) of
$\phi$ over $X$ are called
{\em $f$-centers} of the set $A$.
\par
We present an existence theorem for $f$-centers, based on compactness in
the so called $ball$-topology and on the Fatou property of $f$.
We discuss sufficient conditions for the assumptions being
satisfied. The last section is devoted to significant particular cases:
generalized integral medians, generalized
Chebyshev centers, and ``generalized centers with neglect''''.
Tipologia IRIS:
01 - Articolo su periodico
Elenco autori:
L. Vesely
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