A proximal algorithm with quasi distance. Application to habit's formation

Abstract

We consider a proximal algorithm with quasi distance applied to nonconvex and nonsmooth functions involving analytic properties for a minimization problem. We show the behavioural importance of this proximal point model for the formation of habit in Decision and Making Sciences. The convergence of the sequence generated by our algorithm to a critical-limit point is guaranteed under standard conditions of coercivity and by using the Kurdyka–Łojasiewicz inequality. We present a definition of habit that contemplates that kind of convergence.

Keywords:

• variational analysis
• quasi distance
• Kurdyka–Łojasiewicz inequality
• proximal method
• costs to change
• inertia
• anchoring effect

AMS Subject Classifications::

• 65K10
• 90C26
• 49J53
• 49M27
• 90C30
• 90B50

Acknowledgements

The authors wish to thank the anonymous referees for carefully reading this article and providing valuable comments and suggestions which helped us improve the presentation. The first author was supported by CAPES/CNPq – IEL Nacional – Brasil.