Displaying similar documents to “Long-term planning versus short-term planning in the asymptotical location problem”

On optimal matching measures for matching problems related to the Euclidean distance

José Manuel Mazón, Julio Daniel Rossi, Julián Toledo (2014)

Mathematica Bohemica

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We deal with an optimal matching problem, that is, we want to transport two measures to a given place (the target set) where they will match, minimizing the total transport cost that in our case is given by the sum of two different multiples of the Euclidean distance that each measure is transported. We show that such a problem has a solution with an optimal matching measure supported in the target set. This result can be proved by an approximation procedure using a p -Laplacian system....

Vector variational problems and applications to optimal design

Pablo Pedregal (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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We examine how the use of typical techniques from non-convex vector variational problems can help in understanding optimal design problems in conductivity. After describing the main ideas of the underlying analysis and providing some standard material in an attempt to make the exposition self-contained, we show how those ideas apply to a typical optimal desing problem with two different conducting materials. Then we examine the equivalent relaxed formulation to end up with a new problem...

Asymptotics of an optimal compliance-location problem

Giuseppe Buttazzo, Filippo Santambrogio, Nicolas Varchon (2006)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the problem of placing a Dirichlet region made by small balls of given radius in a given domain subject to a force in order to minimize the compliance of the configuration. Then we let tend to infinity and look for the Γ-limit of suitably scaled functionals, in order to get informations on the asymptotical distribution of the centres of the balls. This problem is both linked to optimal location and shape optimization problems.

A variational model for urban planning with traffic congestion

Guillaume Carlier, Filippo Santambrogio (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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We propose a variational model to describe the optimal distributions of residents and services in an urban area. The functional to be minimized involves an overall transportation cost taking into account congestion effects and two aditional terms which penalize concentration of residents and dispersion of services. We study regularity properties of the minimizers and treat in details some examples.

On the infimum convolution inequality

R. Latała, J. O. Wojtaszczyk (2008)

Studia Mathematica

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We study the infimum convolution inequalities. Such an inequality was first introduced by B. Maurey to give the optimal concentration of measure behaviour for the product exponential measure. We show how IC inequalities are tied to concentration and study the optimal cost functions for an arbitrary probability measure μ. In particular, we prove an optimal IC inequality for product log-concave measures and for uniform measures on the ℓ ⁿ p balls. Such an optimal inequality implies, for a...

Gradient flows in Wasserstein spaces and applications to crowd movement

Filippo Santambrogio (2010-2011)

Séminaire Équations aux dérivées partielles

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Starting from a motivation in the modeling of crowd movement, the paper presents the topics of gradient flows, first in ℝ n , then in metric spaces, and finally in the space of probability measures endowed with the Wasserstein distance (induced by the quadratic transport cost). Differently from the usual theory by Jordan-Kinderlehrer-Otto and Ambrosio-Gigli-Savaré, we propose an approach where the optimality conditions for the minimizers of the optimization problems that one solves at every...

Gradient flows in Wasserstein spaces and applications to crowd movement

Filippo Santambrogio (2009-2010)

Séminaire Équations aux dérivées partielles

Similarity:

Starting from a motivation in the modeling of crowd movement, the paper presents the topics of gradient flows, first in ℝ n , then in metric spaces, and finally in the space of probability measures endowed with the Wasserstein distance (induced by the quadratic transport cost). Differently from the usual theory by Jordan-Kinderlehrer-Otto and Ambrosio-Gigli-Savaré, we propose an approach where the optimality conditions for the minimizers of the optimization problems that one solves at every...

Synchronized traffic plans and stability of optima

Marc Bernot, Alessio Figalli (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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The irrigation problem is the problem of finding an efficient way to transport a measure μ onto a measure μ. By efficient, we mean that a structure that achieves the transport (which, following [Bernot, Caselles and Morel, (2005) 417–451], we call traffic plan) is better if it carries the mass in a grouped way rather than in a separate way. This is formalized by considering costs functionals that favorize this property. The aim of this paper is to introduce a dynamical...