Journal of Optimization Theory and Applications

, Volume 171, Issue 1, pp 209–227 | Cite as

Dual Descent Methods as Tension Reduction Systems

  • Glaydston de Carvalho Bento
  • João Xavier da Cruz Neto
  • Antoine Soubeyran
  • Valdinês Leite de Sousa Júnior


In this paper, driven by applications in Behavioral Sciences, wherein the speed of convergence matters considerably, we compare the speed of convergence of two descent methods for functions that satisfy the well-known Kurdyka–Lojasiewicz property in a quasi-metric space. This includes the extensions to a quasi-metric space of both the primal and dual descent methods. While the primal descent method requires the current step to be more or less half of the size of the previous step, the dual approach considers more or less half of the previous decrease in the objective function to be minimized. We provide applications to the famous “Tension systems approach” in Psychology.


Dual descent Inexact proximal Worthwhile change Kurdyka–Lojasiewicz property Tension systems Variational rationality 

Mathematics Subject Classification

90C30 49M29 



The work was supported by CAPES and CNPq.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Glaydston de Carvalho Bento
    • 1
  • João Xavier da Cruz Neto
    • 2
  • Antoine Soubeyran
    • 3
  • Valdinês Leite de Sousa Júnior
    • 1
  1. 1.IMEUniversidade Federal de GoiásGoiâniaBrazil
  2. 2.DMUniversidade Federal do PiauíTeresinaBrazil
  3. 3.Aix-Marseille School of Economics, CNRS and EHESSAix-Marseille UniversityMarseilleFrance

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