Pareto solutions as limits of collective traps: an inexact multiobjective proximal point algorithm

Glaydston Carvalho Bento (1) , João Xavier da Cruz Neto (2) , L. Meireles (3) , Antoine Soubeyran (4)

1 UFG - Universidade Federal de Goiás [Goiânia]
2 UFPI - Universidade Federal do Piauí
3 Instituto Federal Goiano
4 AMSE - Aix-Marseille Sciences Economiques

In this paper we introduce a definition of approximate Pareto efficient solution as well as a necessary condition for such solutions in the multiobjective setting on Riemannian manifolds. We also propose an inexact proximal point method for nonsmooth multiobjective optimization in the Riemannian context by using the notion of approximate solution. The main convergence result ensures that each cluster point (if any) of any sequence generated by the method is a Pareto critical point. Furthermore, when the problem is convex on a Hadamard manifold, full convergence of the method for a weak Pareto efficient solution is obtained. As an application, we show how a Pareto critical point can be reached as a limit of traps in the context of the variational rationality approach of stay and change human dynamics.

Keywords: Multiobjective proximal method; Riemannian manifold; Approximate solution; Variational rationality; Worthwhile moveTrap

Domains: Economics and Finance; Mathematics [math]

Glaydston Carvalho Bento, João Xavier da Cruz Neto, L. Meireles, Antoine Soubeyran. Pareto solutions as limits of collective traps: an inexact multiobjective proximal point algorithm. Annals of Operations Research, 2022, 316 (2), pp.1425-1443. ⟨10.1007/s10479-022-04719-y⟩. ⟨hal-03680291⟩