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Generalized Inexact Proximal Algorithms: Routine’s Formation with Resistance to Change, Following Worthwhile Changes

  • G. C. Bento
  • A. Soubeyran
Article

Abstract

This paper shows how, in a quasi-metric space, an inexact proximal algorithm with a generalized perturbation term appears to be a nice tool for Behavioral Sciences (Psychology, Economics, Management, Game theory,...). More precisely, the new perturbation term represents an index of resistance to change, defined as a “curved enough” function of the quasi-distance between two successive iterates. Using this behavioral point of view, the present paper shows how such a generalized inexact proximal algorithm can modelize the formation of habits and routines in a striking way. This idea comes from a recent “variational rationality approach” of human behavior which links a lot of different theories of stability (habits, routines, equilibrium, traps,...) and changes (creations, innovations, learning and destructions,...) in Behavioral Sciences and a lot of concepts and algorithms in variational analysis.

Keywords

Nonconvex optimization Kurdyka–Lojasiewicz inequality Inexact proximal algorithms Habits Routines Worthwhile changes 

Mathematics Subject Classification

49J52 49M37 65K10 90C30 91E10 

Notes

Acknowledgments

The work was supported by CAPES, CAPES-MES-CUBA 226/2012, FAPEG 201210267000909–05/2012 and CNPq Grants 458479/2014-4, 471815/2012-8, 303732/2011-3, 236938/2012-6.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Universidade Federal de GoiásGoiâniaBrazil
  2. 2.CNRS & EHESSAix-Marseille University (Aix-Marseille School of Economics)MarseilleFrance

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