Kuratowski convergence of the efficient sets in the parametric linear vector semi-infinite optimization |
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| Affiliation: | 1. Escuela Técnica Superior de Ingenieros de Sistemas Informáticos, Universidad Politécnica de Madrid, Calle Alan Turing s/n (Carretera de Valencia Km 7), 28031 Madrid, Spain;2. Facultad de Matemáticas, Universidad Complutense de Madrid, Plaza Ciencias 3, 28040 Madrid, Spain;3. Departamento de Álgebra, Geometría y Topología, Facultad de Ciencias, Universidad de Málaga, Campus de Teatinos s/n, 29071 Málaga, Spain;1. Istituto Nazionale di Geofisica e Vulcanologia, Roma, Italy;2. Universität Wien, Institut für Meteorologie und Geophysik, Vienna, Austria;3. Geophysics Section, School of Cosmic Physics, Dublin Institute for Advanced Studies, Dublin, Ireland;4. Yale University, Department of Geology and Geophysics, New Haven, CT, USA;1. Center for Network Big Data and Decision-Making, Business School, Sichuan University, Chengdu 610065, China;2. Andalusian Research Institute on Data Science and Computational Intelligence (DaSCI), University of Granada, Granada 18071, Spain;3. Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah 21589, Saudi Arabia |
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| Abstract: | In the space of whole linear vector semi-infinite optimization problems we consider the mappings putting into correspondence to each problem the set of efficient and weakly efficient points, respectively. We endow the image space with Kuratowski convergence and by means of the lower and upper semi-continuity of these mappings we prove generic well-posedness of the vector optimization problems. The connection between the continuity and some properties of the efficient sets is also discussed. |
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