Currently displaying 1 – 5 of 5

Showing per page

Order by Relevance | Title | Year of publication

$\text{Γ}$-convergence for a class of functionals with deviating argument.

Journal of Convex Analysis

Optimal transportation networks as free Dirichlet regions for the Monge-Kantorovich problem

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

In the paper the problem of constructing an optimal urban transportation network in a city with given densities of population and of workplaces is studied. The network is modeled by a closed connected set of assigned length, while the optimality condition consists in minimizing the Monge-Kantorovich functional representing the total transportation cost. The cost of trasporting a unit mass between two points is assumed to be proportional to the distance between them when the transportation is carried...

Long-term planning versus short-term planning in the asymptotical location problem

ESAIM: Control, Optimisation and Calculus of Variations

Given the probability measure $\nu$ over the given region $\Omega \subset {ℝ}^{n}$, we consider the optimal location of a set $\Sigma$ composed by $n$ points in $\Omega$ in order to minimize the average distance $\Sigma ↦{\int }_{\Omega }\mathrm{dist}\left(x,\Sigma \right)\phantom{\rule{0.166667em}{0ex}}\mathrm{d}\nu$ (the classical optimal facility location problem). The paper compares two strategies to find optimal configurations: the long-term one which consists in placing all $n$ points at once in an optimal position, and the short-term one which consists in placing the points one by one adding at each step at most one point and preserving...

Long-term planning short-term planning in the asymptotical location problem

ESAIM: Control, Optimisation and Calculus of Variations

Given the probability measure over the given region $\Omega \subset {ℝ}^{n}$, we consider the optimal location of a set composed by points in in order to minimize the average distance $\Sigma ↦{\int }_{\Omega }\mathrm{dist}\phantom{\rule{0.166667em}{0ex}}\left(x,\Sigma \right)\phantom{\rule{0.166667em}{0ex}}\mathrm{d}\nu$ (the classical optimal facility location problem). The paper compares two strategies to find optimal configurations: the long-term one which consists in placing all points at once in an optimal position, and the short-term one which consists in placing the points one by one adding at each step at most one point and preserving the...

Page 1