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On the Dynamics of a Differential Inclusion Built upon a Nonconvex Constrained Minimization Problem

Author

Listed:
  • P. Nistri

    (University of Siena)

  • M. Quincampoix

    (Université de Bretagne)

Abstract

In this paper, we study the dynamics of a differential inclusion built upon a nonsmooth, not necessarily convex, constrained minimization problem in finite-dimensional spaces. In particular, we are interested in the investigation of the asymptotic behavior of the trajectories of the dynamical system represented by the differential inclusion. Under suitable assumptions on the constraint set and the two involved functions (one defining the constraint set, the other representing the functional to be minimized), it is proved that all the trajectories converge to the set of the constrained critical points. We present also a large class of constraint sets satisfying our assumptions. As a simple consequence, in the case of a smooth convex minimization problem, we have that any trajectory converges to the set of minimizers.

Suggested Citation

  • P. Nistri & M. Quincampoix, 2005. "On the Dynamics of a Differential Inclusion Built upon a Nonconvex Constrained Minimization Problem," Journal of Optimization Theory and Applications, Springer, vol. 124(3), pages 659-672, March.
    • Handle: RePEc:spr:joptap:v:124:y:2005:i:3:d:10.1007_s10957-004-1179-7
    DOI: 10.1007/s10957-004-1179-7
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    References listed on IDEAS

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    1. J. Bolte, 2003. "Continuous Gradient Projection Method in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 119(2), pages 235-259, November.
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