Second order optimality conditions for differentiable multiobjective problems
RAIRO - Operations Research - Recherche Opérationnelle, Volume 34 (2000) no. 4, p. 411-426
@article{RO_2000__34_4_411_0,
     author = {Bigi, Giancarlo and Castellani, Marco},
     title = {Second order optimality conditions for differentiable multiobjective problems},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     publisher = {EDP-Sciences},
     volume = {34},
     number = {4},
     year = {2000},
     pages = {411-426},
     zbl = {1039.90063},
     mrnumber = {1815071},
     language = {en},
     url = {http://www.numdam.org/item/RO_2000__34_4_411_0}
}
Bigi, Giancarlo; Castellani, Marco. Second order optimality conditions for differentiable multiobjective problems. RAIRO - Operations Research - Recherche Opérationnelle, Volume 34 (2000) no. 4, pp. 411-426. http://www.numdam.org/item/RO_2000__34_4_411_0/

1. J. Abadie, On the Kuhn-Tucker Theorem, in Nonlinear programming, edited by J. Abadie. North Holland, Amsterdam (1967) 21-36. | MR 218116 | Zbl 0183.22803

2. B. Aghezzaf and M. Hachimi, Second-order optimality conditions in multiobjective optimization problems. J. Optim. Theory Appl. 102 (1999) 37-50. | MR 1702841 | Zbl 1039.90062

3. J.P. Aubin and H. Frankowska, Set-valued analysis. Birkhäuser, Boston (1990). | MR 1048347 | Zbl 1168.49014

4. A. Ben-Tal, Second-order and related extremality conditions in nonlinear programming. J. Optim. Theory Appl. 31 (1980) 143-165. | MR 600379 | Zbl 0416.90062

5. G. Bigi and M. Pappalardo, Regularity conditions for the linear separation of sets. J. Optim. Theory Appl. 99 (1998) 533-540. | MR 1657049 | Zbl 0911.90297

6. B.D. Craven, Nonsmooth multiobjective programming, Numer. Funct. Anal. Optim. 10 (1989) 49-64. | MR 978802 | Zbl 0645.90076

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. | MR 1789120 | Zbl 0985.49005

8. M. Guignard, Generalized Kuhn-Tucker conditions for mathernatical programming problems in a Banach space. SIAM J. Control 7 ( 1969 ) 232-241. | MR 252042 | Zbl 0182.53101

9. J. Jahn, Mathernatical vector optimization in partially ordered linear spaces. Peter Lang, Frankfurt (1986). | MR 830661 | Zbl 0578.90048

10. H. Kawasaki, Second-order necessary conditions of the Kuhn-Tucker type under new constraint qualification. J. Optim, Theory Appl. 57 (1988) 253-264. | MR 938874 | Zbl 0621.90074

11. P. Kanniappan, Necessary conditions for optimality of nondifferentiable convex multiobjective programming. J. Optim. Theory Appl. 40 (1983) 167-174. | MR 703314 | Zbl 0488.49007

12. J.G. Lin, Maximal vectors and multi-objective optimization. J. Optim, Theory Appl. 18 (1976) 41-64. | MR 418945 | Zbl 0298.90056

13. T. Maeda, Constraint qualifications in multiobjective optimization problems: Differentiable case. J. Optim, Theory Appl. 80 (1994) 483-500. | MR 1265172 | Zbl 0797.90083

14. A.A.K. Majumdar, Optimality conditions in differentiable multiobjective programming. J. Optim. Theory Appl. 92 (1997) 419-427. | MR 1430022 | Zbl 0886.90122

15. O.L. Mangasarian, Nonlinear programming. Mc Graw-Hill, New York (1969). | MR 252038 | Zbl 0527.00013

16. I. Marusciac, On Fritz John type optimality criterion in multi-objective optimization. Anal. Numér. Théor. Approx, 11 (1982) 109-114. | MR 692476 | Zbl 0501.90081

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. | MR 728312 | Zbl 0502.90076

18. J.P. Penot, Optimality conditions in mathematical programming and composite optimization. Math. Programming 67 (1994) 225-245. | MR 1305567 | Zbl 0828.90137

19. V. Preda, On some sufficient optimality conditions in multiobjective differentiable programming. Kybernetica (Prague) 28 (1992) 263-270. | MR 1183618 | Zbl 0784.90070

20. Y. Sawaragi, H. Nakayama and T. Tanino Theory of multiobjective optimization. Academic, Orlando (1985). | MR 807529 | Zbl 0566.90053

21. C. Singh, Optimality conditions in multiobjective differentiable programming. J. Optim, Theory Appl. 53 (1987) 115-123. | MR 889214 | Zbl 0593.90071

22. S.Y. Wang, A note on optimality conditions in multiobjective programming. Systems Sci. Math. Sci. 1 (1988) 184-190. | MR 1009139 | Zbl 0727.90065

23. S.Y. Wang, Second order necessary and sufficient conditions in multiobjective programming. Numer. Funct Anal, Optim, 12 (1991) 237-252. | MR 1125051 | Zbl 0764.90076

24. S.Y. Wang and Z.F. Li, Scalarization and Lagrange duality in multiobjective optimization. Optimization 26 (1992) 315-324. | MR 1236615 | Zbl 0817.90100

25. S.Y. Wang and F.M. Yang, A gap between multiobjective optimization and scalar optimization. J. Optim. Theory Appl. 68 (1991) 389-391. | MR 1091499 | Zbl 0696.90062

26. D.E. Ward, Calculus for parabolic second-order derivatives. Set-Valued Anal. 1 (1993) 213-246. | MR 1249264 | Zbl 0797.58014

27. D.E. Ward, A chain rule for parabolic second-order epiderivatives. Optimization 28 (1994) 223-236. | MR 1275978 | Zbl 0816.49010

28. L. Zemin, The optimality conditions of differentiable vector optimization problems. J. Math. Anal. Appl. 201 (1996) 35-43. | MR 1397884 | Zbl 0851.90105