Support separation theorems and their applications to vector surrogate reverse duality
Kybernetika, Tome 28 (1992) no. 2, pp. 140-154 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Classification : 49J27, 49N15, 90C29
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     title = {Support separation theorems and their applications to vector surrogate reverse duality},
     journal = {Kybernetika},
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     year = {1992},
     volume = {28},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_1992_28_2_a5/}
}
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Chien, Tran Quoc. Support separation theorems and their applications to vector surrogate reverse duality. Kybernetika, Tome 28 (1992) no. 2, pp. 140-154. http://geodesic.mathdoc.fr/item/KYB_1992_28_2_a5/

[1] R. B: Holmes: Geometrical Functional Analysis and Its Applications. Springer-Verlag, New York - Heidelberg - Berlin 1975. | MR

[2] I. Ekeland, R. Temam: Analyse Convexe et Problemes Variationelles. Dunod, Paris 1974.

[3] J. Bair: On the convex programming problem in an ordered vector space. Bull. Soc. Royal Science LIEGE 46 (1977), 234 - 240. | MR | Zbl

[4] E. G. Golstein: Duality Theory in Mathematical Programming and Its Applications. Nauka, Moscow 1971. In Russian. | MR

[5] V. V. Podinovskij, V.D. Nogin: Pareto optimal solutions in multiobjective problems. Nauka, Moscow 1982. In Russian.

[6] G.S. Rubinstein: Duality in mathematical programming and some questions of convex analysis. Uspekhi mat. nauk 25 (1970), 5, 155, 171 - 201. In Russian. | MR

[7] M. Vlach: On necessary conditions of optimality in linear spaces. Comment. Math. Univ. Carol. 11 (1970), 3, 501 - 503. | MR | Zbl

[8] M. Vlach: A separation theorem for finite families. Comment. Math. Univ. Carol. 12 (1971), 4, 655 - 670. | MR | Zbl

[9] M. Vlach: A note on separation by linear mappings. Comment. Math. Univ. Carol. 18 (1977), 1, 167 - 168. | MR | Zbl

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

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

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

[13] Tran Quoc Chien: Fenchel-Lagrange duality in vector fractional programming via abstract duality scheme. Kybernetika 23 (1986), 4, 299 - 319. | MR | Zbl

[14] Tran Quoc Chien: Parturbation theory of duality in vector optimization via abstract duality scheme. Kybernetika 23 (1987), 1, 67 - 81. | MR

[15] I. Singer: Optimization by level set methods VI: Generalization of surrogate type reverse convex duality. Optimization 18 (1987), 4, 485 - 499. | MR

[16] I. Singer: Maximization of lower semicontinuous convex functionals on bounded subsets of locally convex spaces I: Hyperplane theorems. Appl. Math. Optim. 5 (1979), 349 - 362. | MR

[17] I. Singer: A general theory of surrogate dual and perturbational extended surrogate dual optimization problems. J. Math. Anal. Appl. 104 (1984), 351 - 389. | MR | Zbl

[18] I. Singer: Surrogate dual problems and surrogate Lagrangians. J. Math. Anal. Appl. 98 (1984), 31 - 71. | MR | Zbl

[19] J.-E. Martinez Legaz, I. Singer: Surrogate duality for vector optimization. Numer. Funct. Anal. Optim. 9 (1987), 5-6, 544-568. | MR | Zbl

[20] I. Singer: Minimization of continuous convex functionals on complements of convex subsets of locally convex space. Math. Operationsforsch. Statist. Ser. Optim. 11 (1980), 221 - 234. | MR

[21] I. Singer: Extension with larger norm and separation with double support in normed linear spaces. Bull. Austral. Math. Soc. 21 (1980), 93 - 105. | MR

[22] I. Singer: Optimization and best approximation. In: Nonlinear Analysis, Theory and Applications (R. Kluge, ed.), Abh. Akad. Wiss. DDR, Berlin 1981, pp. 275 - 285. | MR | Zbl