On the Lexicographic Centre of Multiple Objective Optimization

Zhang Jiangao () and Shitao Yang ()
Additional contact information
Zhang Jiangao: Chongqing University
Shitao Yang: Florida Institute of Technology

Journal of Optimization Theory and Applications, 2016, vol. 168, issue 2, No 12, 600-614

Abstract: Abstract We study the lexicographic centre of multiple objective optimization. Analysing the lexicographic-order properties yields the result that, if the multiple objective programming’s lexicographic centre is not empty, then it is a subset of all efficient solutions. It exists if the image set of multiple objective programming is bounded below and closed. The multiple objective linear programming’s lexicographic centre is nonempty if and only if there exists an efficient solution to the multiple objective linear programming. We propose a polynomial-time algorithm to determine whether there is an efficient solution to multiple objective linear programming, and we solve the multiple objective linear programming’s lexicographic centre by calculating at most the same number of dual linear programs as the number of objective functions and a system of linear inequalities.

Keywords: Multiple objective programming; Lexicographic order; Lexicographic centre; Efficient solution; Image set; $$\theta $$ θ -image set; 49M29; 65K05; 90C05; 90C29; 90C47 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-015-0810-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:168:y:2016:i:2:d:10.1007_s10957-015-0810-0

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-015-0810-0

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().