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
2 LJAD - Laboratoire Jean Alexandre Dieudonné
3 MAS - Mathématiques Appliquées aux Systèmes - EA 4037
4 SIMPAF - SImulations and Modeling for PArticles and Fluids

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.

Domaines: Equations aux dérivées partielles [math.AP]

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⟩