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The lovebirds problem: why solve Hamilton-Jacobi-Bellman equations matters in love affairs

Thierry Goudon 1, 2 Pauline Lafitte 3, 4
1 COFFEE - COmplex Flows For Energy and Environment
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR7351
4 SIMPAF - SImulations and Modeling for PArticles and Fluids
LPP - Laboratoire Paul Painlevé - UMR 8524, Inria Lille - Nord Europe
Abstract : The lovebirds problem consists in finding the compromise between well-being and efforts that are necessary to sustain a durable sentimental relationship. According to a modeling introduced by J.-M. Rey, the problem can be cast as to find the data for a certain dynamical system, guaranteeing that the associated trajectory belongs to the stable manifold. We further discuss the interpretation by means of the Dynamical Programming Principle and the Hamilton-Jacobi-Bellman framework. It allows us to propose an algorithm to determine numerically the solution of the lovebirds problem.
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Thierry Goudon, Pauline Lafitte. The lovebirds problem: why solve Hamilton-Jacobi-Bellman equations matters in love affairs. Acta Applicandae Mathematicae, Springer Verlag, 2015, 136 (1), pp.147-165. ⟨10.1007/s10440-014-9944-6⟩. ⟨hal-00780945⟩

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