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Duality in vector optimization. III: Vector partially quasiconcave programming and vector fractional programming. (English) Zbl 0575.49007

[For part II see the paper reviewed above.]
The so-called \(T_ 2\)-duality concept for a certain class of vector optimization programs is introduced. Further, both the \(T_ 1\)-duality theory and the \(T_ 2\)-duality theory are applied for some classes of vector fractional programming. Finally, for completeness, some \(T_ 1\)- duality theorems are formulated and proved in the last section.

MSC:

49N15 Duality theory (optimization)
52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
90C32 Fractional programming
49J45 Methods involving semicontinuity and convergence; relaxation
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References:

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[2] Tran Quoc Chien: Duality in vector optimization. Part II. Vector quasiconcave programming. Kybernetika 20 (1984), 5, 386-404. · Zbl 0575.49006
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