Lower semicontinuous regularization for vector-valued mappings

Journal of Global Optimization

Volumn 35, Issue 2, 2006, Pages 283-309

  Mansour, M Ait ^a   Metrane, A ^b   Thera M ^a  

^a UNIVERSITY OF LIMOGES   (France)

^b ÉCOLE POLYTECHNIQUE DE MONTRÉAL   (Canada)

Author keywords

D.C. mappings; Lower level set; Lower semicontinuous regularization; Vector lower limit; Vector valued mappings

Indexed keywords

D.C.-MAPPINGS; LOWER LEVEL SET; LOWER SEMICONTINUOUS REGULARIZATION; VECTOR LOWER LIMIT; VECTOR-VALUED MAPPINGS;

GEOMETRY; SET THEORY; TOPOLOGY; VECTORS;

CONFORMAL MAPPING;

EID: 33745437485     PISSN: 09255001     EISSN: 15732916     Source Type: Journal    
DOI: 10.1007/s10898-005-3839-z     Document Type: Article

References (25)

1. Akian, M. (1999), Densities of idempotent measures and large deviations, Transactions of the American Mathematical Society 351, 4515-4543.
2. Akian, M. and Singer, I. (2003), Topologies on lattice ordered groups, separations from closed downwards and conjugations of type Lau, Optimization 52(6), 629-673.
3. Borwein, J.M. (2004), Cones and orderings, private communication.
4. Borwein, J.M. and Théra, M. (1992), Sandwich theorems for semicontinuous operators, Canadian Mathematical Bulletin 35(4), 463-474.
5. Brézis, H. (1983), Analyse fonctionnelle: Théorie et applications, MASSON Paris New York Barcelone Milan Mexico Sao Paulo.
6. Combari, C., Laghdir, M. and Thibault, L. (1994), Sous- différentiel de fonctions convexes composées, Annals of Science and Mathematics Québec 18(2), 119-148.
7. Ellaia, R. and Hiriart-Urruty, J.B. (1986), The conjugate of difference of convex functions, JOTA 49(3).
8. Elhilali Alaoui, A. (1996), Caractérisation des fonctions D.C. Annals of Science and Mathematics Québec. 20(1), 1-13.
9. Fremlin, D.H. (1974), Topological Riesz Spaces and Measure Theory, Lectures in Mathematics, University of Essex.
10. Gerritse, G. (1997), Lattice-valued semicontinuous functions, Probability and lattices, CWI Tract 110, Math. Centrum, Centrum Wisk., Inform., Amsterdam pp. 93-125.
11. Gierz, G., Hoffmann, K.H., Keimel, K., Lawason, J.D, Mislove, M. and Scott, D.S. (1980), A Compendium of Continuous Lattices, Springer-Verlag, Berlin, Heidelberg, New York.
12. Holwerda, H. (1989), Closed Hypographs, Semicontinuity and the Topological Closed-Graph Theorem, A Unifying Approach, Report 8935, Catholic University of Nijmegen.
13. Lemaire, B. and Volle, M. (1998), Duality in D.C. programming, in Nonconvex Optimization and Its Applications, 27, Kluwer Academic Publishers, Dordrecht, 331-345.
14. Luc, D.T. (1989), Theory of Vector Optimization, Springer-Verlag, Berlin, Heidelberg, New-York, London, Paris, Tokyo.
15. Martinez-Legaz, J. and Volle, M. (1999), Duality in D.C. programming: the case of several D.C. constraints, Journal of Mathematical Analysis and Applications 237(2), 657-671.
16. Metrane, A. (2003), Applications vectorielles s'écrivant comme différence de fonctions convexes et optimisation sur l'ensemble efficient, Thèse de doctorat, Université Cadi Ayyad, Faculté des Sciences Samlalia, Marrakech.
17. Muselli, E. (2000), Upper and lower semicontinuity for set-valued mappings involving constraints, JOTA 106(3), 527-550.
18. Penot, J.-P. and Théra, M. (1979), Semi-continuité des applications et des multiapplication, C.R. Acad. Sci. Paris Série A, 419-422.
19. Penot, J.-P. and Théra, M. (1982), Semi-continuous mappings in general topology, Archiv der Mathematics 38, 158-166.
20. Peressini, A.L. (1967), Ordered Topological Vector Spaces, Harper's series in modern mathematics, New-York.
21. Rockafellar, R.T. and Wets, R. J-B. (1998), Variational Analysis, Springer-Verlag, Berlin, Heidelberg, New-York.
22. Rubinov, A. (2000), Abstract Convexity and Global Optimization, Kluwer Academic Publishers, Dordrecht.
23. Schaefer, H.H. (1974), Banach Lattices and Positive Operators, Springer-Verlag, Berlin, Heidelberg, New-York.
24. Théra, M. (1978), Étude des Fonctions Convexes Vectorielles Semi-Continues, Doctorat de Troisième Cycle, N 76, Université de Pau et des Pays de L'Adour.
25. Théra, M. (1981), Subdifferential calculus for convex operators, Journal of Mathematical Analysis and Applications 80(1), 78-91.