Dual Descent Methods as Tension Reduction Systems

Glaydston de Carvalho Bento, João Xavier da Cruz Neto, Antoine Soubeyran and Valdinês Leite de Sousa Júnior
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Glaydston de Carvalho Bento: UFG - Universidade Federal de Goiás [Goiânia]
João Xavier da Cruz Neto: UFPI - Universidade Federal do Piauí
Valdinês Leite de Sousa Júnior: UFG - Universidade Federal de Goiás [Goiânia]

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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.

Date: 2016-10
Note: View the original document on HAL open archive server: https://amu.hal.science/hal-01690176
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Published in Journal of Optimization Theory and Applications, 2016, 171 (1), pp.209 - 227. ⟨10.1007/s10957-016-0994-y⟩

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Journal Article: Dual Descent Methods as Tension Reduction Systems (2016)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01690176

DOI: 10.1007/s10957-016-0994-y

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