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

In: Recent Advances in Optimization

Author

Listed:
  • Felipe Alvarez

    (Universidad de Chile)

  • Alexandre Cabot

    (Université de Limoges)

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.

Suggested Citation

  • Felipe Alvarez & Alexandre Cabot, 2006. "On the Asymptotic Behavior of a System of Steepest Descent Equations Coupled by a Vanishing Mutual Repulsion," Lecture Notes in Economics and Mathematical Systems, in: Alberto Seeger (ed.), Recent Advances in Optimization, pages 3-17, Springer.
    • Handle: RePEc:spr:lnechp:978-3-540-28258-7_1
    DOI: 10.1007/3-540-28258-0_1
    as

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