Abstract
Using the Fenchel-Rockafellar approach for the convex mathematical programming problem with inequality constraints different dual optimization problems by means of distinct perturbations of the primal problem are derived and studied. The classical Lagrange dual problem is one of those dual problems obtained by the perturbation of the right hand side of the inequality constraints. For the various dual problems equality/inequality relations between the optimum values are verified under appropriate assumptions. Moreover, the duality relations to the primal problem are considered, in particular strong duality. Using the dual problems some optimality conditions are established.
The results are illustrated by some examples.
The application and usefulness for the construction of general multiobjective dual problems to the general multiobjective convex optimization problem is mentioned.
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References
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Wanka G., Boţ R.-I. (2001) A new duality approach for multiobjective convex optimization problems. Fakultät für Mathematik, TU Chemnitz, Preprint 2001–6
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© 2002 Springer-Verlag Berlin Heidelberg
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Wanka, G., Boţ, RI. (2002). On the Relations Between Different Dual Problems in Convex Mathematical Programming. In: Chamoni, P., Leisten, R., Martin, A., Minnemann, J., Stadtler, H. (eds) Operations Research Proceedings 2001. Operations Research Proceedings 2001, vol 2001. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-50282-8_32
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DOI: https://doi.org/10.1007/978-3-642-50282-8_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43344-6
Online ISBN: 978-3-642-50282-8
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