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 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.