  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. In this variational context,
the perturbation term represents a specific instance of the very general
concept of resistance to change, which is the disutility of some inconvenients
to change. Central to the analysis are the original variational concepts of
"worthwhile changes" and "marginal worthwhile stays". At the behavioral level,
this paper advocates that proximal algorithms are well suited to modelize the
emergence of habituation/routinized human behaviors. We show when, and at which
speed, a "worthwhile to change" process converges to a behavioral trap.
