Second order optimality conditions for differentiable multiobjective problems
RAIRO - Operations Research - Recherche Opérationnelle, Volume 34 (2000) no. 4, pp. 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},
     pages = {411--426},
     publisher = {EDP-Sciences},
     volume = {34},
     number = {4},
     year = {2000},
     mrnumber = {1815071},
     zbl = {1039.90063},
     language = {en},
     url = {http://archive.numdam.org/item/RO_2000__34_4_411_0/}
}
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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://archive.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 | Zbl

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

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

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

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

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

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 | Zbl

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

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

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 | Zbl

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

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

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

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

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

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

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 | Zbl

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

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

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

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

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

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

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

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 | Zbl

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

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

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