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Perturbation theory of duality in vector optimization via the abstract duality scheme. (English) Zbl 0615.49007
The perturbation theory of duality has been usually constructed with help of the theory of conjugate functions. In this paper, unlike the traditional method, two kinds of perturbation duality in vector optimization are suggested on the basis of an abstract duality scheme. This approach is much simpler than the one using a generalization of conjugate functions in the vector case. It gives, however, almost the same or, in some cases, stronger results. The classical Fenchel duality is also generalized for maximizing a sum of a (instead of \(n=2\) in other works) concave functions. The only mathematical tool is separation of n convex sets.

MSC:
49N15 Duality theory (optimization)
49K40 Sensitivity, stability, well-posedness
90C31 Sensitivity, stability, parametric optimization
90C25 Convex programming
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References:
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