Journal of Convex Analysis 30 (2023), No. 4, 1155--1172
Copyright Heldermann Verlag 2023
Periodic and Attraction-Stifling Behavior in Numerical Minimization
Adam B. Levy
Dept. of Mathematics, Bowdoin College, College Station, Brunswick, U.S.A.
alevy@bowdoin.edu
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].
Keywords: Numerical minimization, attraction, periodic iterate-multisets, minvalue-monotonicity, pseudo-distance, nearly periodic iterate-multisets, attraction-stifling.
MSC: 49J53.
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