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About duality and alternative in multi-objective optimization. (English) Zbl 0597.90086
McLinden’s result on the equivalence between a theorem of the alternative and a duality theorem for constrained optimization problems [see L. McLinden, Proc. Amer. Math. Soc. 53, 172-175 (1975; Zbl 0308.90046)] is extended to the multiobjective case. We then discuss some existing results on that topic and present an alternative approach to duality relations in conditionally complete lattices.

MSC:
90C31 Sensitivity, stability, parametric optimization
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References:
[1] McLinden, L.,Duality Theorems and Theorems of the Alternative, Proceedings of the American Mathematical Society, Vol. 5, pp. 172-175, 1975. · Zbl 0287.90031
[2] Rosinger, E. E.,Duality and Alternative in Multiobjective Optimization, Proceedings of the American Mathematical Society, Vol. 64, pp. 307-312, 1977. · Zbl 0333.49030
[3] Luc, D. T.,On Duality Theory in Multiobjective Programming, Journal of Optimization Theory and Applications, Vol. 43, pp. 557-582, 1984. · Zbl 0517.90076
[4] Azimov, A. Ja.,Duality in Vector Optimization Problems, Soviet Mathematics Doklady, Vol. 26, pp. 170-174, 1982. · Zbl 0508.49014
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