Inégalités variationnelles non convexes

Messaoud Bounkhel; Djalel Bounkhel

ESAIM: Control, Optimisation and Calculus of Variations (2005)

  • Volume: 11, Issue: 4, page 574-594
  • ISSN: 1292-8119

Abstract

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In this paper we propose several algorithms of the projection type to solve a new class of nonconvex variational problems. This class generalizes many types of variational inequalities (Cho et al. (2000), Noor (1992), Zeng (1998), Stampacchia (1964)) from the convex case to the nonconvex case. The sensitivity of this class of nonconvex variational problems is also studied.

How to cite

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Bounkhel, Messaoud, and Bounkhel, Djalel. "Inégalités variationnelles non convexes." ESAIM: Control, Optimisation and Calculus of Variations 11.4 (2005): 574-594. <http://eudml.org/doc/245504>.

@article{Bounkhel2005,
abstract = {Dans cet article nous proposons différents algorithmes pour résoudre une nouvelle classe de problèmes variationels non convexes. Cette classe généralise plusieurs types d’inégalités variationnelles (Cho et al. (2000), Noor (1992), Zeng (1998), Stampacchia (1964)) du cas convexe au cas non convexe. La sensibilité de cette classe de problèmes variationnels non convexes a été aussi étudiée.},
author = {Bounkhel, Messaoud, Bounkhel, Djalel},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {ensembles uniformément réguliers; problèmes variationnels non convexes; uniformly regular set; nonconvex variational problems; prox-regularity},
language = {fre},
number = {4},
pages = {574-594},
publisher = {EDP-Sciences},
title = {Inégalités variationnelles non convexes},
url = {http://eudml.org/doc/245504},
volume = {11},
year = {2005},
}

TY - JOUR
AU - Bounkhel, Messaoud
AU - Bounkhel, Djalel
TI - Inégalités variationnelles non convexes
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2005
PB - EDP-Sciences
VL - 11
IS - 4
SP - 574
EP - 594
AB - Dans cet article nous proposons différents algorithmes pour résoudre une nouvelle classe de problèmes variationels non convexes. Cette classe généralise plusieurs types d’inégalités variationnelles (Cho et al. (2000), Noor (1992), Zeng (1998), Stampacchia (1964)) du cas convexe au cas non convexe. La sensibilité de cette classe de problèmes variationnels non convexes a été aussi étudiée.
LA - fre
KW - ensembles uniformément réguliers; problèmes variationnels non convexes; uniformly regular set; nonconvex variational problems; prox-regularity
UR - http://eudml.org/doc/245504
ER -

References

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  3. [3] M. Bounkhel and L. Thibault, Further characterizations of regular sets in Hilbert spaces and their applications to nonconvex sweeping process. Preprint, Centro de Modelamiento Matematico (CMM), Universidad de Chile (2000). Submitted to J. Nonlinear Convex Anal. MR2159846
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  9. [9] M.A. Noor, General algorithm for variational inequalities. J. Optim. Theory Appl. 73 (1992) 409–413. Zbl0794.49009
  10. [10] P.D. Panagiotopoulos and G.E. Stavroulakis, New types of variational principles based on the notion of quasidifferentiability. Acta Mech. 94 (1992) 171–194. Zbl0756.73096
  11. [11] R.A. Poliquin, R.T. Rockafellar and L. Thibault, Local differentiability of distance functions. Trans. Amer. Math. Soc. 352 (2000) 5231–5249. Zbl0960.49018
  12. [12] R.T. Rockafellar and R. Wets, Variational Analysis. Springer-Verlag, Berlin (1998). Zbl0888.49001MR1491362
  13. [13] G. Stampacchia, Formes bilinéaires coercives sur les ensembles convexes. C. R. Acad. Sci. Paris 258 (1964) 4413–4416. Zbl0124.06401
  14. [14] L.C. Zeng, On a general projection algorithm for variational inequalities. J. Optim. Theory Appl. 97 (1998) 229–235. Zbl0907.90265

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