Dual Descent Methods as Tension Reduction Systems

Glaydston Carvalho Bento (), João Xavier Cruz Neto (), Antoine Soubeyran and Valdinês Leite Sousa Júnior ()
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Glaydston Carvalho Bento: Universidade Federal de Goiás
João Xavier Cruz Neto: Universidade Federal do Piauí
Valdinês Leite Sousa Júnior: Universidade Federal de Goiás

Journal of Optimization Theory and Applications, 2016, vol. 171, issue 1, No 10, 209-227

Abstract: Abstract 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.

Keywords: Dual descent; Inexact proximal; Worthwhile change; Kurdyka–Lojasiewicz property; Tension systems; Variational rationality; 90C30; 49M29 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-016-0994-y

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