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

G. C. Bento () and Antoine Soubeyran
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G. C. Bento: Universidade Federal de Goiás

Journal of Optimization Theory and Applications, 2015, vol. 166, issue 1, No 8, 172-187

Abstract: 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; 49J52; 49M37; 65K10; 90C30; 91E10 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (10)

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DOI: 10.1007/s10957-015-0711-2

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