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Arrow-Barankin-Blackwell theorems and related results in cone duality: A survey. (English) Zbl 0982.90048
Nguyen, Van Hien (ed.) et al., Optimization. Proceedings of the 9th Belgian-French-German conference, Namur, Belgium, September 7-11, 1998. Berlin: Springer. Lect. Notes Econ. Math. Syst. 481, 119-131 (2000).
Summary: We attempt a brief survey on the cone duality and on the density theorems of Arrow-Barankin and Blackwell’s type [K. Arrow, E. Barankin and D. Blackwell, Contrib. Theory of Games II, Ann. Math. Studies 28, 87-91 (1953; Zbl 0050.14203)]. Concerning the latter aspect we show the equivalence of two recent and ostensibly different results. We follow a unified approach which provides in particular a simple way of surveying these results an their proofs.
For the entire collection see [Zbl 0935.00054].

MSC:
90C29 Multi-objective and goal programming
90C46 Optimality conditions and duality in mathematical programming
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