Inexact Multi-Objective Local Search Proximal Algorithms: Application to Group Dynamic and Distributive Justice Problems
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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.
KeywordsMulti-objective Inexact proximal Group dynamic Distributive justice Behavioral sciences Variational rationality
Mathematics Subject Classification90C29 90C30 49M30
The work was supported by CAPES, CNPq, MathAmSud (CAPES) 88881.117595/2016-01 and the ANR GREEN-Econ research project (ANR-16-CE03-0005).
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