| Title:
|
Support separation theorems and their applications to vector surrogate reverse duality (English) |
| Author:
|
Chien, Tran Quoc |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
28 |
| Issue:
|
2 |
| Year:
|
1992 |
| Pages:
|
140-154 |
| . |
| Category:
|
math |
| . |
| MSC:
|
49J27 |
| MSC:
|
49N15 |
| MSC:
|
90C29 |
| idZBL:
|
Zbl 0770.49004 |
| idMR:
|
MR1169216 |
| . |
| Date available:
|
2009-09-24T18:31:01Z |
| Last updated:
|
2012-06-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125774 |
| . |
| Reference:
|
[1] R. B: Holmes: Geometrical Functional Analysis and Its Applications.Springer-Verlag, New York - Heidelberg - Berlin 1975. MR 0410335 |
| Reference:
|
[2] I. Ekeland, R. Temam: Analyse Convexe et Problemes Variationelles.Dunod, Paris 1974. |
| Reference:
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[3] J. Bair: On the convex programming problem in an ordered vector space.Bull. Soc. Royal Science LIEGE 46 (1977), 234 - 240. Zbl 0378.90079, MR 0493762 |
| Reference:
|
[4] E. G. Golstein: Duality Theory in Mathematical Programming and Its Applications.Nauka, Moscow 1971. In Russian. MR 0322531 |
| Reference:
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[5] V. V. Podinovskij, V.D. Nogin: Pareto optimal solutions in multiobjective problems.Nauka, Moscow 1982. In Russian. |
| Reference:
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[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 0293989 |
| Reference:
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[7] M. Vlach: On necessary conditions of optimality in linear spaces.Comment. Math. Univ. Carol. 11 (1970), 3, 501 - 503. Zbl 0206.12005, MR 0288603 |
| Reference:
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[8] M. Vlach: A separation theorem for finite families.Comment. Math. Univ. Carol. 12 (1971), 4, 655 - 670. Zbl 0229.52008, MR 0290126 |
| Reference:
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[9] M. Vlach: A note on separation by linear mappings.Comment. Math. Univ. Carol. 18 (1977), 1, 167 - 168. Zbl 0345.52001, MR 0433328 |
| Reference:
|
[10] Tran Quoc Chien: Duality in vector optimization. Part I: Abstract duality scheme.Kybernetika 20 (1984), 4, 304-313. MR 0768510 |
| Reference:
|
[11] Tran Quoc Chien: Duality in vector optimization. Part II: Vector quasiconcave programming.Kybernetika 20 (1984), 5, 386 - 404. MR 0776328 |
| Reference:
|
[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 0777980 |
| Reference:
|
[13] Tran Quoc Chien: Fenchel-Lagrange duality in vector fractional programming via abstract duality scheme.Kybernetika 23 (1986), 4, 299 - 319. Zbl 0616.90081, MR 0868023 |
| Reference:
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[14] Tran Quoc Chien: Parturbation theory of duality in vector optimization via abstract duality scheme.Kybernetika 23 (1987), 1, 67 - 81. MR 0883908 |
| Reference:
|
[15] I. Singer: Optimization by level set methods VI: Generalization of surrogate type reverse convex duality.Optimization 18 (1987), 4, 485 - 499. MR 0909657 |
| Reference:
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[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 0551081 |
| Reference:
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[17] I. Singer: A general theory of surrogate dual and perturbational extended surrogate dual optimization problems.J. Math. Anal. Appl. 104 (1984), 351 - 389. Zbl 0607.90089, MR 0766133 |
| Reference:
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[18] I. Singer: Surrogate dual problems and surrogate Lagrangians.J. Math. Anal. Appl. 98 (1984), 31 - 71. Zbl 0584.49006, MR 0728516 |
| Reference:
|
[19] J.-E. Martinez Legaz, I. Singer: Surrogate duality for vector optimization.Numer. Funct. Anal. Optim. 9 (1987), 5-6, 544-568. Zbl 0609.49012, MR 0895984 |
| Reference:
|
[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 0640688 |
| Reference:
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[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 0569090 |
| Reference:
|
[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. Zbl 0472.41023, MR 0639931 |
| . |
