Vector duality for convex vector optimization problems by means of the quasi-interior of the ordering cone |
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Authors: | Sorin-Mihai Grad Emilia-Loredana Pop |
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Affiliation: | 1. Department of Mathematics, Chemnitz University of Technology, Chemnitz, Germany.grad@mathematik.tu-chemnitz.de;3. Faculty of Mathematics and Computer Science, Babe?-Bolyai University, Cluj-Napoca, Romania. |
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Abstract: | We define weakly minimal elements of a set with respect to a convex cone by means of the quasi-interior of the cone and characterize them via linear scalarization, generalizing the classical weakly minimal elements from the literature. Then we attach to a general vector optimization problem, a dual vector optimization problem with respect to (generalized) weakly efficient solutions and establish new duality results. By considering particular cases of the primal vector optimization problem, we derive vector dual problems with respect to weakly efficient solutions for both constrained and unconstrained vector optimization problems and the corresponding weak, strong and converse duality statements. |
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Keywords: | quasi-interior weakly minimal element weakly efficient solution vector duality |
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