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Inexact Multi-Objective Local Search Proximal Algorithms: Application to Group Dynamic and Distributive Justice Problems

Abstract : We introduce and examine an inexact multi-objective proximal method with a proximal distance as the perturbation term. Our algorithm utilizes a local search descent process that eventually reaches a weak Pareto optimum of a multi-objective function, whose components are the maxima of continuously differentiable functions. Our algorithm gives a new formulation and resolution of the following important distributive justice problem in the context of group dynamics: In each period, if a group creates a cake, the problem is, for each member, to get a high enough share of this cake; if this is not possible, then it is better to quit, breaking the stability of the group.
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https://hal-amu.archives-ouvertes.fr/hal-01985329
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Submitted on : Tuesday, February 1, 2022 - 6:03:57 PM
Last modification on : Wednesday, February 2, 2022 - 11:42:38 AM
Long-term archiving on: : Tuesday, May 3, 2022 - 8:41:43 AM

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Glaydston de Carvalho Bento, Orizon Pereira Ferreira, Antoine Soubeyran, Valdinês Leite De Sousa Júnior. Inexact Multi-Objective Local Search Proximal Algorithms: Application to Group Dynamic and Distributive Justice Problems. Journal of Optimization Theory and Applications, Springer Verlag, 2018, 177 (1), pp.181-200. ⟨10.1007/s10957-018-1258-9⟩. ⟨hal-01985329⟩

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