Second order optimality conditions for differentiable multiobjective problems
Giancarlo Bigi; Marco Castellani
RAIRO - Operations Research - Recherche Opérationnelle (2000)
- Volume: 34, Issue: 4, page 411-426
- ISSN: 0399-0559
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topBigi, Giancarlo, and Castellani, Marco. "Second order optimality conditions for differentiable multiobjective problems." RAIRO - Operations Research - Recherche Opérationnelle 34.4 (2000): 411-426. <http://eudml.org/doc/105228>.
@article{Bigi2000,
author = {Bigi, Giancarlo, Castellani, Marco},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
language = {eng},
number = {4},
pages = {411-426},
publisher = {EDP-Sciences},
title = {Second order optimality conditions for differentiable multiobjective problems},
url = {http://eudml.org/doc/105228},
volume = {34},
year = {2000},
}
TY - JOUR
AU - Bigi, Giancarlo
AU - Castellani, Marco
TI - Second order optimality conditions for differentiable multiobjective problems
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 2000
PB - EDP-Sciences
VL - 34
IS - 4
SP - 411
EP - 426
LA - eng
UR - http://eudml.org/doc/105228
ER -
References
top- 1. J. ABADIE, On the Kuhn-Tucker Theorem, in Nonlinear programming, edited by J. Abadie. North Holland, Amsterdam (1967) 21-36. Zbl0183.22803MR218116
- 2. B. AGHEZZAF and M. HACHIMI, Second-order optimality conditions in multiobjective optimization problems. J. Optim. Theory Appl. 102 (1999) 37-50. Zbl1039.90062MR1702841
- 3. J.P. AUBIN and H. FRANKOWSKA, Set-valued analysis. Birkhäuser, Boston (1990). Zbl1168.49014MR1048347
- 4. A. BEN-TAL, Second-order and related extremality conditions in nonlinear programming. J. Optim. Theory Appl. 31 (1980) 143-165. Zbl0416.90062MR600379
- 5. G. BIGI and M. PAPPALARDO, Regularity conditions for the linear separation of sets. J. Optim. Theory Appl. 99 (1998) 533-540. Zbl0911.90297MR1657049
- 6. B.D. CRAVEN, Nonsmooth multiobjective programming, Numer. Funct. Anal. Optim. 10 (1989) 49-64. Zbl0645.90076MR978802
- 7. F. GIANNESSI, G. MASTROEN and L. PELLEGRINI, On the theory of vector optimization and variational inequalities. Image space analysis and separation, in Vector variational inequalities and vector equilibria, edited by F. Giannessi. Kluwer, Dordrecht (2000) 141-201. Zbl0985.49005MR1789120
- 8. M. GUIGNARD, Generalized Kuhn-Tucker conditions for mathernatical programming problems in a Banach space. SIAM J. Control 7 ( 1969 ) 232-241. Zbl0182.53101MR252042
- 9. J. JAHN, Mathernatical vector optimization in partially ordered linear spaces. Peter Lang, Frankfurt (1986). Zbl0578.90048MR830661
- 10. H. KAWASAKI, Second-order necessary conditions of the Kuhn-Tucker type under new constraint qualification. J. Optim, Theory Appl. 57 (1988) 253-264. Zbl0621.90074MR938874
- 11. P. KANNIAPPAN, Necessary conditions for optimality of nondifferentiable convex multiobjective programming. J. Optim. Theory Appl. 40 (1983) 167-174. Zbl0488.49007MR703314
- 12. J.G. LIN, Maximal vectors and multi-objective optimization. J. Optim, Theory Appl. 18 (1976) 41-64. Zbl0298.90056MR418945
- 13. T. MAEDA, Constraint qualifications in multiobjective optimization problems: Differentiable case. J. Optim, Theory Appl. 80 (1994) 483-500. Zbl0797.90083MR1265172
- 14. A.A.K. MAJUMDAR, Optimality conditions in differentiable multiobjective programming. J. Optim. Theory Appl. 92 (1997) 419-427. Zbl0886.90122MR1430022
- 15. O.L. MANGASARIAN, Nonlinear programming. Mc Graw-Hill, New York (1969). Zbl0527.00013MR252038
- 16. I. MARUSCIAC, On Fritz John type optimality criterion in multi-objective optimization. Anal. Numér. Théor. Approx, 11 (1982) 109-114. Zbl0501.90081MR692476
- 17. M. MINAMI, Weak Pareto-optimal necessary conditions in a nondifferentiable multiobjective program on a Banach space. J. Optim, Theory Appl. 41 (1983). 451-461. Zbl0502.90076MR728312
- 18. J.P. PENOT, Optimality conditions in mathematical programming and composite optimization. Math. Programming 67 (1994) 225-245. Zbl0828.90137MR1305567
- 19. V. PREDA, On some sufficient optimality conditions in multiobjective differentiable programming. Kybernetica (Prague) 28 (1992) 263-270. Zbl0784.90070MR1183618
- 20. Y. SAWARAGI, H. NAKAYAMA and T. TANINOTheory of multiobjective optimization. Academic, Orlando (1985). Zbl0566.90053MR807529
- 21. C. SINGH, Optimality conditions in multiobjective differentiable programming. J. Optim, Theory Appl. 53 (1987) 115-123. Zbl0593.90071MR889214
- 22. S.Y. WANG, A note on optimality conditions in multiobjective programming. Systems Sci. Math. Sci. 1 (1988) 184-190. Zbl0727.90065MR1009139
- 23. S.Y. WANG, Second order necessary and sufficient conditions in multiobjective programming. Numer. Funct Anal, Optim, 12 (1991) 237-252. Zbl0764.90076MR1125051
- 24. S.Y. WANG and Z.F. Li, Scalarization and Lagrange duality in multiobjective optimization. Optimization 26 (1992) 315-324. Zbl0817.90100MR1236615
- 25. S.Y. WANG and F.M. YANG, A gap between multiobjective optimization and scalar optimization. J. Optim. Theory Appl. 68 (1991) 389-391. Zbl0696.90062MR1091499
- 26. D.E. WARD, Calculus for parabolic second-order derivatives. Set-Valued Anal. 1 (1993) 213-246. Zbl0797.58014MR1249264
- 27. D.E. WARD, A chain rule for parabolic second-order epiderivatives. Optimization 28 (1994) 223-236. Zbl0816.49010MR1275978
- 28. L. ZEMIN, The optimality conditions of differentiable vector optimization problems. J. Math. Anal. Appl. 201 (1996) 35-43. Zbl0851.90105MR1397884
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