A practical approach to approximate bilinear functions in mathematical programming problems by using Schur's decomposition and SOS type 2 variables

S A Gabriel (), R García-Bertrand, P Sahakij and A J Conejo
Additional contact information
S A Gabriel: University of Maryland
R García-Bertrand: Universidad de Castilla – La Mancha
P Sahakij: University of Maryland
A J Conejo: Universidad de Castilla – La Mancha

Journal of the Operational Research Society, 2006, vol. 57, issue 8, 995-1004

Abstract: Abstract This paper provides a new methodology to solve bilinear, non-convex mathematical programming problems by a suitable transformation of variables. Schur's decomposition and special ordered sets (SOS) type 2 constraints are used resulting in a mixed integer linear or quadratic program in the two applications shown. While Beale, Tomlin and others developed the use of SOS type 2 variables to handle non-convexities, our approach is novel in two aspects. First, the use of Schur's decomposition as an integral part of the approximation step is new and leads to a numerically viable method to separate the variables. Second, the combination of our approach for handling bilinear side constraints in a complementarity or equilibrium problem setting is also new and opens the way to many interesting and realistic modifications to such models. We contrast our approach with other methods for solving bilinear problems also known as indefinite quadratic programs. From a practical point of view our methodology is helpful since no specialized procedures need to be created so that existing solvers can be used. The approach is illustrated with two engineering examples and the mathematical analysis appears in the Appendices.

Keywords: optimization; engineering; non-linear programming; linear programming; integer programming (search for similar items in EconPapers)
Date: 2006
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

Downloads: (external link)
http://link.springer.com/10.1057/palgrave.jors.2602052 Abstract (text/html)
Access to full text is restricted to subscribers.

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:pal:jorsoc:v:57:y:2006:i:8:d:10.1057_palgrave.jors.2602052

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/41274

DOI: 10.1057/palgrave.jors.2602052

Access Statistics for this article

Journal of the Operational Research Society is currently edited by Tom Archibald and Jonathan Crook

More articles in Journal of the Operational Research Society from Palgrave Macmillan, The OR Society
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().