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

Glaydston de Carvalho Bento , Orizon Pereira Ferreira , Antoine Soubeyran (1) , Valdinês Leite De Sousa Júnior

1 AMSE - Aix-Marseille Sciences Economiques

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.

Domains: Economics and Finance

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, 2018, 177 (1), pp.181-200. ⟨10.1007/s10957-018-1258-9⟩. ⟨hal-01985329⟩