Dual Descent Methods as Tension Reduction Systems

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• 作者：Glaydston de Carvalho Bento…
• 关键词：Dual descent ; Inexact proximal ; Worthwhile change ; Kurdyka–Lojasiewicz property ; Tension systems ; Variational rationality
• 刊名：Journal of Optimization Theory and Applications
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：171
• 期：1
• 页码：209-227
• 全文大小：520 KB
• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operations Research/Decision Theory;
• 出版者：Springer US
• ISSN：1573-2878
• 卷排序：171

文摘

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.