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

Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05

Volumn 2005, Issue , 2005, Pages 5832-5836

  Nistri, Paolo ^a   Quincampoix, Marc ^b  

^a UNIVERSITY OF SIENA   (Italy)

^b UNIVERSITÉ DE BRETAGNE OCCIDENTALE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; OPTIMIZATION; TRAJECTORIES;

DIFFERENTIAL INCLUSION; MULTIVALUED VECTORS; NONSMOOTH CONSTRAINED OPTIMIZATION PROBLEMS; TRAJECTORIES CONVERGES;

CONTROL SYSTEM ANALYSIS;

EID: 33847215093     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2005.1583093     Document Type: Conference Paper

References (16)

1. J.-P. Aubin and A. Cellina, Differential Inclusions, Springer Verlag, 1984.
2. J.-P. Aubin, Viability Theory, Birkhäuser, 1991.
3. A. Bacciotti and F. Ceragioli, Nonsmooth optimal regulation and discontinuous stabilization, Abstr. Appl. Anal., Vol. 2003, (2003), 1159-1195.
4. E. Bierstone and P. Milman, Semianalytic and subanalytic sets, Inst. Hautes Études Sci. Publ. Math., 67, (1988), 5-42.
5. J. Boite, On the continuous gradient projection method in Hilbert spaces Journal of Optimization Theory and Applications, 119, (2003), 235-259.
6. J. Bolte, A. Danilidis and A. Lewis, The Lojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems. Preprint available at the WEB site: pareto.uab.es/~adaniilidis.
7. J. Bolte, A. Danilidis and A. Lewis, The Morse-Sard theorem for non-differentiable subanalytic functions. Preprint available at at the WEB site: pareto.uab.es/~adaniilidis.
8. M. Forti, P. Nistri and M. Quincampoix, Generalized Neural Network for Nonsmooth Nonlinear Programming Problems IEEE Transactions on Circuits and Systems, 51, (2004), 1741-1754.
9. S. Lojasiewicz, Sur les trajectoires du gardient d'une fonction analytique, Seminari di Geometria 1982-83, Università di Bologna, Istituto di Geometria, Dipartimento di Matematica, (1984) 115-117.
10. S. Lojasiewicz, Une propriété topologique des sous-ensembles analytiques réels. Les équations aux Dérivées Partielles Editions du Centre National de la Recherche Scientifique, Paris (1963) 87-89.
11. S. Lojasiewicz, Sur la géométrie semi- et sous-analytique. Ann. Inst. Fourier (Grenoble) 43 no. 5, (1993), 1575-1595.
12. P. Nistri and M. Quincampoix, On Open-Loop and Feedback Attainability of a Closed Set for Nonlinear Control Systems, Journal of Mathematical Analysis and Applications, 270, (2002), 474-487.
13. P. Nistri and M. Quincampoix, On the Dynamics of a Differential Inclusion built upon a Nonconvex Constrained Minimization Problem, Journal of Optimization Theory and Appl., 124, (2005), 659-672.
14. T. Rockafellar and R. Wets, Variational Analysis, Springer-Verlag, 1997.
15. O. Serea, On Reflecting Boundary Problem for Optimal Control, SIAM Journal of Control and Optimization, 42, (2003), 559-575.
16. L. Van den Dries and C. Miller, Geometric categories and o-minimal structures, Duke Math. J., 2, (1996), 497-540.