[en] The set obtained by adding all cuts whose validity follows from a maximal lattice free polyhedron with max-facet-width at most w is called the w th split closure. We show the w th split closure is a polyhedron. This generalizes a previous result showing this to be true when w = 1. We also consider the design of finite cutting plane proofs for the validity of an inequality. Given a measure of “size” of a maximal lattice free polyhedron, a natural question is how large a size s of a maximal lattice free polyhedron is required to design a finite cutting plane proof for the validity of an inequality. We characterize s based on the faces of the linear relaxation of the mixed integer linear set.
Disciplines :
Mathematics
Author, co-author :
Andersen, Kent; Otto-von-Guericke Universität Magdeburg > Institut für Mathematische Optimierung
Louveaux, Quentin ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Optimisation discrète
Weismantel, Robert; Otto-von-Guericke Universituat Magdeburg > Institut für Mathematische Optimierung
Language :
English
Title :
An analysis of mixed integer linear sets based on lattice point free convex sets
scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.
Bibliography
Andersen, K., G. Cornuéjols, Y. Li. 2005. Split closure and intersection cuts. Math. Programming Ser. A 102 457-493.
Andersen, K., Q. Louveaux, R. Weismantel. 2008. Certificates of linear mixed integer infeasibility. Oper. Res. Lett.
Balas, E. 1971 Intersection cuts-A new type of cutting plane for integer programming. Oper. Res. 19 19-39.
Balas, E. 1979. Disjunctive programming. Ann. Discrete Math. 5 517-546.
Cook, W. J., R. Kannan, A. Schrijver. 1990. Chvátal closures for mixed integer programming problems. Math. Programming 47 155-174.
Cornuéjols, G. 2008. Valid inequalities for mixed integer linear programs. Math. Programming Ser. B 112 3-44.
Lovász, L. 1989. Geometry of numbers and integer programming. M. Iri, K. Tanabe, eds. Math. Programming, Recent Developments and Applications. Kluwer, Dordrecht, The Netherlands, 177-210.
Rockafellar, R. T. 1970. Convex Analysis. Princeton University Press, Princeton, NJ.
Similar publications
Sorry the service is unavailable at the moment. Please try again later.
This website uses cookies to improve user experience. Read more
Save & Close
Accept all
Decline all
Show detailsHide details
Cookie declaration
About cookies
Strictly necessary
Performance
Strictly necessary cookies allow core website functionality such as user login and account management. The website cannot be used properly without strictly necessary cookies.
This cookie is used by Cookie-Script.com service to remember visitor cookie consent preferences. It is necessary for Cookie-Script.com cookie banner to work properly.
Performance cookies are used to see how visitors use the website, eg. analytics cookies. Those cookies cannot be used to directly identify a certain visitor.
Used to store the attribution information, the referrer initially used to visit the website
Cookies are small text files that are placed on your computer by websites that you visit. Websites use cookies to help users navigate efficiently and perform certain functions. Cookies that are required for the website to operate properly are allowed to be set without your permission. All other cookies need to be approved before they can be set in the browser.
You can change your consent to cookie usage at any time on our Privacy Policy page.