Math. Program., Ser. A https://doi.org/10.1007/s10107-018-1299-8 FULL LENGTH PAPER 1 2 Michele Conforti · Laurence A. Wolsey Received: 12 August 2016 / Accepted: 16 May 2018 © Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2018 Abstract Given polyhedron P and and a point x , the separation problem for polyhe- dra asks to certify that x ∈ P and if not, to determine an inequality that is satisﬁed by P and violated by x . This problem is repeatedly solved in cutting plane methods for Integer Programming and the quality of the violated inequality is an essential feature in the performance of such methods. In this paper we address the problem of ﬁnding efﬁciently an inequality that is violated by x and either deﬁnes an improper face or a facet of P. We show that, by solving a single linear program, one almost surely obtains such an improper face or facet. Keywords Integer programming · Separation problem · Polyhedra · Extended formulations · Facets · Cutting plane algorithm · Split inequalities Mathematics Subject Classiﬁcation 90C27 · 90C57 1 Introduction Given a polyhedron P and a point x ,the separation problem asks to either certify that ∗
Mathematical Programming – Springer Journals
Published: May 28, 2018
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera