NDLI: On the properties of solutions to a differential inclusion associated with a nonsmooth constrained optimization problem

Content Provider	IEEE Xplore Digital Library
Author	Nistri, P. Quincampoix, M.
Copyright Year	2005
Description	Author affiliation: Dipartimento di Ingegneria dell’Informazione, University of Siena, Siena, Italy. pnistri@dii.unisi.it (Nistri, P.)
Abstract	In this paper we consider, under very general conditions, a constrained minimization problem and we associate to this problem a differential inclusion which has the property that all the trajectories converge to the set C of constrained critical points. The conditions on the functional to be minimized and on the function which defines the constraint are the minimal requirements on these data to use the tools of the nonsmooth analysis to show the convergence of the trajectories to C. Furthermore, if these functions are also subanalytic, then it is proved that any trajectory converges to a critical point and it has finite length. In fact, we show that these assumptions guarantee that the multivalued vector field defining the differential inclusion satisfies a Lojasiewicz-type inequality. The dependence of the rate of convergence on the values of the Lojasiewicz exponent is also shown.
Starting Page	5832
Ending Page	5836
File Size	227803
Page Count	5
File Format	PDF
ISBN	0780395670
DOI	10.1109/CDC.2005.1583093
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2005-12-15
Publisher Place	Spain
Access Restriction	Subscribed
Rights Holder	IEEE/EUCA
Subject Keyword	Constraint optimization Convergence Control system analysis Functional analysis Control systems Humans Contracts Difference equations Cost function Quadratic programming
Content Type	Text
Resource Type	Article

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