An analysis of some dual problems in multiobjective optimization (I)

In this work we study the duality for a general multiobjective optimization problem. Considering, first, a scalar problem, different duals using the conjugacy approach are presented. Starting from these scalar duals, we introduce six different multiobjective dual problems to the primal one, one depe...

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Published inOptimization Vol. 53; no. 3; pp. 281 - 300
Main Authors Boţ, R.I., Wanka, G.
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.06.2004
Subjects
Conjugate duality
Mathematics Subject Classifications 1991: 49N15
Multiobjective convex optimization
Pareto-efficiency
Weak and strong duality
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ISSN0233-1934
1029-4945
DOI10.1080/02331930410001715514

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Abstract In this work we study the duality for a general multiobjective optimization problem. Considering, first, a scalar problem, different duals using the conjugacy approach are presented. Starting from these scalar duals, we introduce six different multiobjective dual problems to the primal one, one depending on certain vector parameters. The existence of weak and, under certain conditions, strong duality between the primal and the dual problems is shown. Afterwards, some inclusion results for the image sets of the multiobjective dual problems (D 1 ), (D α ) and (D FL ) are derived. Moreover, we verify that the efficiency sets within the image sets of these problems coincide, but the image sets themselves do not.
AbstractList In this work we study the duality for a general multiobjective optimization problem. Considering, first, a scalar problem, different duals using the conjugacy approach are presented. Starting from these scalar duals, we introduce six different multiobjective dual problems to the primal one, one depending on certain vector parameters. The existence of weak and, under certain conditions, strong duality between the primal and the dual problems is shown. Afterwards, some inclusion results for the image sets of the multiobjective dual problems (D 1 ), (D α ) and (D FL ) are derived. Moreover, we verify that the efficiency sets within the image sets of these problems coincide, but the image sets themselves do not.
Author Boţ, R.I.
Wanka, G.
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10.1007/978-3-642-46368-6_12
10.1007/BF02594784
10.1057/jors.1974.108
10.1017/S000497270000277X
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SubjectTerms Conjugate duality
Mathematics Subject Classifications 1991: 49N15
Multiobjective convex optimization
Pareto-efficiency
Weak and strong duality
Title An analysis of some dual problems in multiobjective optimization (I)
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