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

P. Nistri and M. Quincampoix
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P. Nistri: University of Siena
M. Quincampoix: Université de Bretagne

Journal of Optimization Theory and Applications, 2005, vol. 124, issue 3, No 7, 659-672

Abstract: 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.

Keywords: nonconvex nonsmooth constrained minimization problems; critical points; differential inclusions; viability theory (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s10957-004-1179-7

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