Surrogate duality for vector optimization |
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Authors: | Juan-Enrique Martinez-Legaz Ivan Singer |
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Institution: | 1. Department of Functional Equations , Unviersity of Barcelona , Gran Vía, 585, Barcelona, 08007, Spain;2. Department of Mathematics , INCREST , Bd. P[acaron]cii, Bucharest, 79622, Romania |
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Abstract: | Using our theorems (of 12]) on separation of convex sets by linear operators, in the sense of the lexi-cographical order on Rn, we prove some theorems of surrogate duality for vector optimization problems with convex constraints (but no regularity assumption), where the surrogate constraint sets are generalized half-spaces and the surrogate multipliers are linear operators, or isomorphisms, or isometries. In the cae of inequality constraints, we prove that the surrogate multipliers can be taken lexicographically non-negative isometries or non-negative (in the usual order) linear isomorphisms. |
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