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Journal Articles Acta Applicandae Mathematicae Year : 2015

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

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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Dates and versions

hal-00780945 , version 1 (25-01-2013)

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Thierry Goudon, Pauline Lafitte. The lovebirds problem: why solve Hamilton-Jacobi-Bellman equations matters in love affairs. Acta Applicandae Mathematicae, 2015, 136 (1), pp.147-165. ⟨10.1007/s10440-014-9944-6⟩. ⟨hal-00780945⟩
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