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Some Characterizations of Solution Sets of Vector Optimization Problems with Generalized Order

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Abstract

We establish some necessary and sufficient conditions for optimal solutions to vector optimization problems, where the optimality notion is understood in the sense of generalized order from Mordukhovich (2006, Definition 5.53). Moreover, some criteria for the closedness and the connectedness of the set of generalized order solutions are also given. Many examples are provided to illustrate the obtained results.

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Correspondence to Nguyen Van Tuyen.

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This work is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.01-2014.39. A part of this work was done when the author was working at the Vietnam Institute for Advanced Study in Mathematics (VIASM). He would like to thank the VIASM for providing a fruitful research environment and working condition. The author is indebted to the referee for valuable comments and suggestions.

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Van Tuyen, N. Some Characterizations of Solution Sets of Vector Optimization Problems with Generalized Order. Acta Math Vietnam 41, 677–694 (2016). https://doi.org/10.1007/s40306-015-0162-8

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  • DOI: https://doi.org/10.1007/s40306-015-0162-8

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