On the Asymptotic Behavior of a System of Steepest Descent Equations Coupled by a Vanishing Mutual Repulsion

Felipe Alvarez () and Alexandre Cabot ()
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Felipe Alvarez: Universidad de Chile
Alexandre Cabot: Université de Limoges

A chapter in Recent Advances in Optimization, 2006, pp 3-17 from Springer

Abstract: Summary We investigate the behavior at infinity of a special dissipative system, which consists of two steepest descent equations coupled by a non-autonomous conservative repulsion. The repulsion term is parametrized in time by an asymptotically vanishing factor. We show that under a simple slow parametrization assumption the limit points, if any, must satisfy an optimality condition involving the repulsion potential. Under some additional restrictive conditions, requiring in particular the equilibrium set to be one-dimensional, we obtain an asymptotic convergence result. Finally, some open problems are listed.

Keywords: Steep Descent; Slow Parametrization; Asymptotic Convergence; Steep Descent; Repulsion Term (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:lnechp:978-3-540-28258-7_1

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DOI: 10.1007/3-540-28258-0_1

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