Duality in vector optimization. II: Vector quasiconcave programming. (English) Zbl 0575.49006

[For part I see ibid. 20, 304-313 (1984; Zbl 0556.49010).]
On the basis of the abstract theory presented in the first part, a duality theory is developed for the vector quasiconcave programming. In Section 3 some necessary concepts and assertions of (quasi)convexity are introduced. Section 4 deals with the duality theory in vector quasiconcave programming with affine constraints. Finally, in Section 5 a limit approach is proposed to define the dual problems for the vector quasiconcave programming with convex constraints. The third part of this paper is described in the following review.


49N15 Duality theory (optimization)
49K27 Optimality conditions for problems in abstract spaces
90C48 Programming in abstract spaces
47H99 Nonlinear operators and their properties
49J45 Methods involving semicontinuity and convergence; relaxation
52A07 Convex sets in topological vector spaces (aspects of convex geometry)
90C25 Convex programming
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[1] Tran Quoc Chien: Duality in vector optimization. Part 1: Abstract duality scheme. Kybernetika 20 (1984), 3, 304-313. · Zbl 0556.49010
[2] B. Martos: Nonlinear Programming: Theory and Methods. Akadémiai Kiadó, Budapest 1975. · Zbl 0357.90027
[3] G. S. Rubinstein: Separation theorems of convex sets. Sibirsk. Mat. Ž. 5 (1964), 5, 1098-1124. In Russian. · Zbl 0137.15202
[4] V. G. Demjanov, L. V. Vasiljev: Nonsmooth Optimization. Nauka, Moskva 1981. In Russian.
[5] R. Holmes: Geometrical Functional Analysis and Its Applications. Springer-Verlag, Berlin-Heidelberg-New York 1975. · Zbl 0336.46001
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