Dual Descent Methods as Tension Reduction Systems

Dual Descent Methods as Tension Reduction Systems

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Article ID: iaor20163690
Volume: 171
Issue: 1
Start Page Number: 209
End Page Number: 227
Publication Date: Oct 2016
Journal: Journal of Optimization Theory and Applications
Authors: , , ,
Keywords: heuristics, behaviour, social
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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