Abstract

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].

Author information

Contact details are reproduced from the original publication and may be historical.

Adam B. Levy

Dept. of Mathematics, Bowdoin College, College Station, Brunswick, U.S.A.

alevy@bowdoin.edu

Keywords

  • Numerical minimization
  • attraction
  • periodic iterate-multisets
  • minvalue-monotonicity
  • pseudo-distance
  • nearly periodic iterate-multisets
  • attraction-stifling

Mathematics Subject Classification

49J53

Suggested citation

A. B. Levy. “Periodic and Attraction-Stifling Behavior in Numerical Minimization.” Journal of Convex Analysis 30 (2023), No. 4, 1155–1172.

Copyright Heldermann Verlag 2023