Acta Mathematica Vietnamica

, Volume 41, Issue 4, pp 677–694

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

Article

DOI: 10.1007/s40306-015-0162-8

Cite this article as:
Van Tuyen, N. Acta Math Vietnam (2016) 41: 677. doi:10.1007/s40306-015-0162-8
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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.

Keywords

Vector optimizationGeneralized orderNecessary and sufficient optimality conditionClosednessConnectedness

Mathematics Subject Classification (2010)

90C4690C2990C31

Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2016

Authors and Affiliations

  1. 1.Department of MathematicsHanoi Pedagogical University No. 2Phuc YenVietnam