Periodic and Attraction-Stifling Behavior in Numerical Minimization

We introduce and study concepts of "periodic" and "nearly-periodic" to describe and understand specific iterative behaviors related to attraction in numerical minimization. We also introduce a notion of "attraction-stifling" which can signal slow progress toward an attractor. We explore connections between these concepts, as well as how attraction-stifling relates to the categorization presented in a recent paper of the author [Categorizing with catastrophic radii in numerical minimization, Set-Valued Var. Analysis 29 (2021) 1–28].