1. Pareto solutions as limits of collective traps: an inexact multiobjective proximal point algorithm
- Author
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G. C. Bento, J. X. Cruz Neto, L. V. Meireles, A. Soubeyran, Universidade Federal de Goiás [Goiânia] (UFG), Universidade Federal do Piauí (UFPI), Instituto Federal Goiano, Aix-Marseille Sciences Economiques (AMSE), École des hautes études en sciences sociales (EHESS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Fundacao de Amparo a Pesquisa do Estado do Goias (FAPEG) - Grant: 201710267000532, Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPQ)Grant: 308330/2018-8& 314106/2020-0, and Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES)
- Subjects
TheoryofComputation_MISCELLANEOUS ,Variational rationality ,Worthwhile moveTrap ,Riemannian manifold ,General Decision Sciences ,Multiobjective proximal method ,Approximate solution ,[MATH]Mathematics [math] ,Management Science and Operations Research ,[SHS.ECO]Humanities and Social Sciences/Economics and Finance - Abstract
International audience; 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.
- Published
- 2022
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