Synchronized traffic plans and stability of optima

Bernot, Marc; Figalli, Alessio

doi:10.1051/cocv:2008012

Bernot, Marc ; Figalli, Alessio

ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 4, pp. 864-878.

Résumé

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, Publ. Mat. 49 (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 cost functional on traffic plans that we argue to be more realistic. The existence of minimizers is proved in two ways: in some cases, we can deduce it from a classical semicontinuity argument; the other cases are treated by studying the link between our cost and the one introduced in [Bernot, Caselles and Morel, Publ. Mat. 49 (2005) 417-451]. Finally, we discuss the stability of minimizers with respect to specific variations of the cost functional.

MR Zbl

DOI : 10.1051/cocv:2008012

Classification : 49Q20, 90B10, 90B06, 90B20
Mots clés : irrigation problem, traffic plans, dynamical cost, stability

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Bernot, Marc; Figalli, Alessio. Synchronized traffic plans and stability of optima. ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 4, pp. 864-878. doi : 10.1051/cocv:2008012. http://www.numdam.org/articles/10.1051/cocv:2008012/

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