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Zbl 1213.90246
Sach, Pham Huu; Tuan, Le Anh; Minh, Nguyen Ba
Approximate duality for vector quasi-equilibrium problems and applications. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 11, 3994-4004 (2010). ISSN 0362-546X

Summary: We introduce new versions of $\varepsilon$-dual problems of a vector quasi-equilibrium problem with set-valued maps, and we give an $\varepsilon$-duality result between approximate solutions of the primal and dual problems. As the first application of the main result, we obtain an $\varepsilon$-duality for a vector quasi-equilibrium problem whose $\varepsilon$-solutions are understood in the sense of proper efficiency. The second application is devoted to an $\varepsilon$-duality for a vector optimization problem with set-valued maps.

MSC 2000:: *90C33 Complementarity problems
90C46 Optimality conditions, duality
90C29 Multi-objective programming, etc.

Keywords: $\varepsilon$-duality; $\varepsilon$-solution; set-valued map

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