On Optimization over the Efficient Set in Linear Multicriteria Programming

R. Horst, N. V. Thoai (), Y. Yamamoto and D. Zenke
Additional contact information
R. Horst: University of Trier
N. V. Thoai: University of Trier
Y. Yamamoto: University of Tsukuba
D. Zenke: University of Tsukuba

Journal of Optimization Theory and Applications, 2007, vol. 134, issue 3, No 5, 433-443

Abstract: Abstract The efficient set of a linear multicriteria programming problem can be represented by a reverse convex constraint of the form g(z)≤0, where g is a concave function. Consequently, the problem of optimizing some real function over the efficient set belongs to an important problem class of global optimization called reverse convex programming. Since the concave function used in the literature is only defined on some set containing the feasible set of the underlying multicriteria programming problem, most global optimization techniques for handling this kind of reverse convex constraint cannot be applied. The main purpose of our article is to present a method for overcoming this disadvantage. We construct a concave function which is finitely defined on the whole space and can be considered as an extension of the existing function. Different forms of the linear multicriteria programming problem are discussed, including the minimum maximal flow problem as an example.

Keywords: Multicriteria optimization; Optimization over the efficient set; Global optimization; Reverse convex constraint; Minimum maximal flow problem (search for similar items in EconPapers)
Date: 2007
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (9)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-007-9219-8 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:134:y:2007:i:3:d:10.1007_s10957-007-9219-8

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

DOI: 10.1007/s10957-007-9219-8

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 ().