zbMATH — the first resource for mathematics

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.

90C31 Sensitivity, stability, parametric optimization
Full Text: DOI
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.