Efficient solutions in generalized linear vector optimization

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.

KEYWORDS:

• Convex polyhedron
• generalized convex polyhedron
• locally convex Hausdorff topological vector space
• generalized linear vector optimization problem
• solution existence theorem

AMS SUBJECT CLASSIFICATIONS:

• 49N10
• 90C05
• 90C29
• 90C48

Acknowledgements

The author would like to thank Professor Nguyen Dong Yen for his guidance and the anonymous referees for their very careful reading and valuable suggestions.

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

This research was supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) [grant number 101.01-2014.37]; Hanoi National University of Education [grant number SPHN17-02].