Displaying similar documents to “Optimal networks for mass transportation problems”

Asymptotic behavior of solutions of nonlinear difference equations

Janusz Migda (2004)

Mathematica Bohemica

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The nonlinear difference equation x n + 1 - x n = a n ϕ n ( x σ ( n ) ) + b n , ( E ) where ( a n ) , ( b n ) are real sequences, ϕ n ℝ ⟶ ℝ , ( σ ( n ) ) is a sequence of integers and lim n ⟶ ∞ σ ( n ) = ∞ , is investigated. Sufficient conditions for the existence of solutions of this equation asymptotically equivalent to the solutions of the equation y n + 1 - y n = b n are given. Sufficient conditions under which for every real constant there exists a solution of equation () convergent to this constant are also obtained.

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...

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

Alessio Brancolini, Giuseppe Buttazzo, Filippo Santambrogio, Eugene Stepanov (2009)

ESAIM: Control, Optimisation and Calculus of Variations

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Given the probability measure ν over the given region Ω ⊂ ℝ n , we consider the optimal location of a set Σ composed by n points in Ω in order to minimize the average distance Σ ↦ ∫ Ω dist ( x , Σ ) d ν (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...