Efficient solutions in generalized linear vector optimization |
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Authors: | Nguyen Ngoc Luan |
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Institution: | 1. Department of Mathematics and Informatics, Hanoi National University of Education , Hanoi, Vietnam.luannn@hnue.edu.vn |
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Abstract: | This paper establishes several new facts on generalized polyhedral convex sets and shows how they can be used in vector optimization. Among other things, a scalarization formula for the efficient solution sets of generalized linear vector optimization problems is obtained. We also prove that the efficient solution set of a generalized linear vector optimization problem in a locally convex Hausdorff topological vector space is the union of finitely many generalized polyhedral convex sets and it is connected by line segments. |
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Keywords: | Convex polyhedron generalized convex polyhedron locally convex Hausdorff topological vector space generalized linear vector optimization problem solution existence theorem |
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