Nondifferentiable and quasidifferentiable duality in vector optimization theory
Kybernetika, Tome 21 (1985) no. 4, pp. 298-312 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Classification : 49N15, 90C31, 90C32
@article{KYB_1985_21_4_a5,
     author = {Chien, Tran Quoc},
     title = {Nondifferentiable and quasidifferentiable duality in vector optimization theory},
     journal = {Kybernetika},
     pages = {298--312},
     year = {1985},
     volume = {21},
     number = {4},
     mrnumber = {815617},
     zbl = {0579.90091},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_1985_21_4_a5/}
}
TY  - JOUR
AU  - Chien, Tran Quoc
TI  - Nondifferentiable and quasidifferentiable duality in vector optimization theory
JO  - Kybernetika
PY  - 1985
SP  - 298
EP  - 312
VL  - 21
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/KYB_1985_21_4_a5/
LA  - en
ID  - KYB_1985_21_4_a5
ER  - 
%0 Journal Article
%A Chien, Tran Quoc
%T Nondifferentiable and quasidifferentiable duality in vector optimization theory
%J Kybernetika
%D 1985
%P 298-312
%V 21
%N 4
%U http://geodesic.mathdoc.fr/item/KYB_1985_21_4_a5/
%G en
%F KYB_1985_21_4_a5
Chien, Tran Quoc. Nondifferentiable and quasidifferentiable duality in vector optimization theory. Kybernetika, Tome 21 (1985) no. 4, pp. 298-312. http://geodesic.mathdoc.fr/item/KYB_1985_21_4_a5/

[1] V. V. Podinovskij, V. D. Nogin: Pareto Optimal Solutions in Multiobjective Problems. Nauka, Moscow 1982 (in Russian).

[2] T. Tanino: Saddle points and duality in multi-objective programming. Internal. J. System Sci. 13 (1982), 3, 323-335. | MR | Zbl

[3] J. W. Nieuwenhuis: Supremal points and generalized duality. Math. Operationsforsch. Statist. Ser. Optim. 11 (1980), 1, 41-59. | MR | Zbl

[4] T. Tanino, Y Sawaragi: Duality theory in multiobjective programming. J. Optim. Theory Appl. 27 (1979), 4, 509-529. | MR | Zbl

[5] T. Tanino, Y. Sawaragi: Conjugate maps and duality in multiobjective programming. J. Optim. Theory Appl. 31 (1980), 4, 473-499. | MR

[6] S. Brumelle: Duality for multiobjective convex programming. Math. Opуr. Res. 6 (1981), 2, 159-172. | MR

[7] Tran Quoc Chien: Duality and optimally conditions in abstract concave maximization. Kybernetika 21 (1985), 2, 108-117. | MR

[8] Tran Quoc Chien: Duality in vector optimization. Part I: Abstract duality scheme. Kybernetika 20 (1984), 4, 304-313. | MR

[9] Tran Quoc Chien: Duality in vector optimization. Part 2: Vector quasiconcave programming. Kybernetika 20 (1984), 5, 386-404. | MR

[10] Tran Quoc Chien: Duality in vector optimization. Part 3: Partially quasiconcave programming and vector fractional programming. Kybernetika 20 (1984), 6, 458-472. | MR

[11] I. Ekeland, R. Teman: Convex Analysis and Variational Problems. North-Holland, American Elsevier, Amsterdam, New York 1976. | MR

[12] R. Holmes: Geometrical Functional Analysis and its Applications. Springor-Verlag, Berlin 1975.

[13] E. G. Golstein: Duality Theory in Mathematical Programming and its Applications. Nauka. Moscow 1971 (in Russian). | MR

[14] C. Zalinescu: A generalization of the Farkas lemma and applications to convex programming. J. Math. Anal. Applic. 66 (1978), 3, 651-678. | MR | Zbl

[15] B. M. Glover: A generalized Farkas lemma with applications to quasidifferentiable programming. Oper. Res. 26 (1982), 7, 125-141. | MR | Zbl

[16] B. D. Craven: Vector-Valued Optimization. Generalized Concavity in Optimization and Economics. New York 1981, pp. 661 - 687. | Zbl

[17] B. Marios: Nonlinear Programming: Theory and Methods. Akad0miai Kiado, Budapest 1975.

[18] S. Schaible: Fractional programming. Z. Oper. Res. 27 (1983), 39-54. | MR | Zbl

[19] S. Schaible: A Survey of Fractional Programming. Generalized Concavity in Optimization and Economics. New York 1981, pp. 417-440. | Zbl

[20] S. Schaible: Duality in fractional programming: a unified approach. Oper. Res. 24 (1976), 3, 452-461. | MR | Zbl

[21] S. Schaible: Fractional programming I; duality. Manag. Sci. 22 (1976), 8, 858-867. | MR | Zbl

[22] S. Schaible: Analyse und Anwendungen von Quotientenprogrammen. Hein-Verlag, Meisenhein 1978. | MR | Zbl

[23] B. D. Craven: Duality for Generalized Convex Fractional Programs. Generalized Concavity in Optimization and Economics. New York 1984, pp. 473 - 489.

[24] U. Passy: Pseudoduality in mathematical programs with quotients and ratios. J. Optim. Theory Appl. 33 (1981), 325-348. | MR

[25] J. Flachs, M. Pollatschek: Equivalence between a generalized Fenchel duality theorem and a saddle-point theorem for fractional programs. J. Optim. Theory Appl. 37 (1981), I, 23-32. | MR