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Dual Descent Methods as Tension Reduction Systems

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.
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https://hal-amu.archives-ouvertes.fr/hal-01690176
Contributor : Elisabeth Lhuillier <>
Submitted on : Monday, January 22, 2018 - 5:22:30 PM
Last modification on : Wednesday, August 5, 2020 - 3:14:20 AM

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Glaydston de Carvalho Bento, João Xavier da Cruz Neto, Antoine Soubeyran, Valdinês Leite de Sousa Júnior. Dual Descent Methods as Tension Reduction Systems. Journal of Optimization Theory and Applications, Springer Verlag, 2016, 171 (1), pp.209 - 227. ⟨10.1007/s10957-016-0994-y⟩. ⟨hal-01690176⟩

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