Inexact Multi-Objective Local Search Proximal Algorithms: Application to Group Dynamic and Distributive Justice Problems
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).
- 1.Mordukhovich, B.: Variational Analysis and Generalized Differentiation. I. Basic Theory. Grundlehren der Mathematischen Wissenschaften, vol. 330. Springer, Berlin (2006)Google Scholar
- 6.Soubeyran, A.: Variational rationality, a theory of individual stability and change: worthwhile and ambidextry behaviors. GREQAM, Aix-Marseille University, France (2009, Pre-print)Google Scholar
- 7.Soubeyran, A.: Variational rationality and the “unsatisfied man”: routines and the course pursuit between aspirations, beliefs. GREQAM, Aix-Marseille University, France (2010, Pre-print)Google Scholar
- 8.Soubeyran, A: Variational rationality. Worthwhile stay and change approach-avoidance human dynamics ending in traps. GREQAM, Aix-Marseille University, France (2016, Pre-print)Google Scholar
- 19.Rawls, J.: A Theory of Justice. Harvard University Press, Cambridge (1971)Google Scholar
- 20.Lewin, K.: A Dynamic Theory of Personality. McGraw-Hill, New York (1935)Google Scholar
- 21.Lewis, K.: Field theory in Social Science. Harper, New York (1951)Google Scholar
- 22.Townsend, J.T., Busemeyer, J.R.: Approach-avoidance: Return to dynamic decision behavior. The Tulane Flowerree Symposia on Cognition, Psychology Press, In: Current Issues in Cognitive Processes (2014)Google Scholar