Efficient solutions in generalized linear vector optimization. Issue 9 (4th July 2019)

• Record Type: Journal Article
• Authors: Luan, Nguyen Ngoc
• Is Part Of: Applicable analysis. Volume 98:Issue 9(2019)
• Page Start: 1694
• Page End: 1704
• Publication Date: 2019-07-04
• Subjects: Convex polyhedron -- generalized convex polyhedron -- locally convex Hausdorff topological vector space -- generalized linear vector optimization problem -- solution existence theorem; 49N10 -- 90C05 -- 90C29 -- 90C48; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1441992
• Languages: English
• ISSNs: 0003-6811

Abstract

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.