Variational Sets of Perturbation Maps and Applications to Sensitivity Analysis for Constrained Vector Optimization |
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Authors: | N L H Anh P Q Khanh |
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Institution: | 1. Department of Mathematics and Computing, University of Science of Hochiminh City, 227 Nguyen Van Cu, District 5, Hochiminh City, Vietnam 2. Department of Mathematics, International University of Hochiminh City, Linh Trung, Thu Duc, Hochiminh City, Vietnam
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Abstract: | We consider sensitivity analysis in terms of variational sets for nonsmooth vector optimization. First, relations between variational sets, or their minima/weak minima, of a set-valued map and that of its profile map are obtained. Second, given an objective map, relationships between the above sets of this objective map and that of the perturbation map and weak perturbation map are established. Finally, applications to constrained vector optimization are given. Many examples are provided to illustrate the essentialness of the imposed assumptions and some advantages of our results. |
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