Optimization Online


A Generalized Inexact Proximal Point Method for Nonsmooth Functions that Satisfies Kurdyka Lojasiewicz Inequality

Glaydston Bento(glaydston***at***ufg.br)
Antoine Soubeyran(antoine.soubeyran***at***gmail.com)

Abstract: In this paper, following the ideas presented in Attouch et al. (Math. Program. Ser. A, 137: 91-129, 2013), we present an inexact version of the proximal point method for nonsmoth functions, whose regularization is given by a generalized perturbation term. More precisely, the new perturbation term is defined as a "curved enough" function of the quasi distance between two successive iterates, that appears to be a nice tool for Behavioral Sciences (Psychology, Economics, Management, Game theory,...). Our convergence analysis is a extension, of the analysis due to Attouch and Bolte (Math. Program. Ser. B, 116: 5-16, 2009) or, more generally, to Moreno et al. (Optimization, 61:1383-1403, 2011), to an inexact setting of the proximal method which is more suitable from the point of view of applications. We give, in a dynamic setting, a striking application to the famous Nobel Prize Kahneman and Tversky~\cite{Tversky1979}, Tversky and Kahneman~\cite{Tversky1991} "loss aversion effect" in Psychology and Management. This application shows how the strength of resistance to change can impact the speed of formation of an habituation/routinization process.

Keywords: Nonconvex optimization; Kurdyka-Lojasiewicz inequality; Inexact proximal algorithms; Speed convergence

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: Federal University of Goias April2014

Download: [PDF]

Entry Submitted: 04/08/2014
Entry Accepted: 04/08/2014
Entry Last Modified: 04/08/2014

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society