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Tran Quoc Chien

Fenchel-Lagrange duality in vector fractional programming via abstract duality scheme. (English) Zbl 0616.90081

Kybernetika 22, 299-319 (1986).
This paper deals with a generalization of both Fenchel and Lagrange duality in vector fractional programming. In the first section the concepts of maximum and supremal are introduced and discussed. In Section 2 simple abstract duality scheme is presented. The last section is devoted to the so-called Fenchel-Lagrange duality in vector fractional programming which is built up on the basis of the abstract duality scheme and a set separation theorem.

Cited in 3 Reviews
Cited in 5 Documents

MSC:

90C32 Fractional programming
90C31 Sensitivity, stability, parametric optimization

Keywords:

Fenchel and Lagrange duality; vector fractional programming
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\textit{Tran Quoc Chien}, Kybernetika 22, 299--319 (1986; Zbl 0616.90081)
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References:

[1] J. Bair: Structure asymptotique et propriétés de séparation en geometrie convexe. Research Report, Université de Liège, 1984.
[2] A. Cambini, Martein: On the Fenchel-like and Lagrangian Duality in Fractional Programming. Research Report, University di Pisa, 1985. · Zbl 0599.90120
[3] Tran Quoc Chien: Duality in vector optimization, I: abstract duality scheme. Kybernetika 20 (1984), 4, 304-313. · Zbl 0556.49010
[4] Tran Quoc Chien: Duality in vector optimization, II: vector quasiconcave programming. Kybernetika 20 (1984), 5, 386-404. · Zbl 0575.49006
[5] Tran Quoc Chien: Duality in vector optimization, III: vector partially quasiconcave programming and vector fractional programming. Kybernetika 20 (1984), 6, 458-472. · Zbl 0575.49007
[6] Tran Quoc Chien: Nondifferentiable and quasidifferentiable duality in vector optimization theory. Kybernetika 21 (1985), 4, 298-312. · Zbl 0579.90091
[7] Tran Quoc Chien: Duality Theory in Vector Optimization. Ph. D. Thesis, Charles University, Prague 1985. · Zbl 0579.90091
[8] G. Grätzen: Lattice Theory. W. H. Freedman and Company, San Francisco 1971.
[9] R. B. Holmes: Geometrical Functional Analysis and Its Applications. Springer-Verlag, New York 1975.
[10] S. Schaible: Duality in fractional programming: a unified approach. Oper. Res. 24 (1976), 3, 452-461. · Zbl 0348.90120 · doi:10.1287/opre.24.3.452
[11] S. Schaible: Fractional programming I: duality. Management Sci. 22 (1976), 8, 859-867. · Zbl 0338.90050 · doi:10.1287/mnsc.22.8.858
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