Corner polyhedron and intersection cuts

M Conforti, G Cornuéjols, G Zambelli - Surveys in operations research and …, 2011‏ - Elsevier
Four decades ago, Gomory introduced the corner polyhedron as a relaxation of a mixed
integer set in tableau form and Balas introduced intersection cuts for the corner polyhedron …

Theoretical challenges towards cutting-plane selection

SS Dey, M Molinaro - Mathematical Programming, 2018‏ - Springer
While many classes of cutting-planes are at the disposal of integer programming solvers, our
scientific understanding is far from complete with regards to cutting-plane selection, ie, the …

Valid inequalities for structured integer programs

M Conforti, G Cornuéjols, G Zambelli, M Conforti… - Integer …, 2014‏ - Springer
In Chaps. 5 and 6 we have introduced several classes of valid inequalities that can be used
to strengthen integer programming formulations in a cutting plane scheme. All these valid …

On the facets of mixed integer programs with two integer variables and two constraints

G Cornuéjols, F Margot - Mathematical Programming, 2009‏ - Springer
In this paper we consider an infinite relaxation of the mixed integer linear program with two
integer variables, nonnegative continuous variables and two equality constraints, and we …

Round-robin tournaments generated by the circle method have maximum carry-over

E Lambrechts, AMC Ficker, DR Goossens… - Mathematical …, 2018‏ - Springer
Abstract The Circle Method is widely used in the field of sport scheduling to generate
schedules for round-robin tournaments. If in such a tournament, team A played team B in its …

A -Slope Theorem for the -Dimensional Infinite Group Relaxation

A Basu, R Hildebrand, M Koppe, M Molinaro - SIAM Journal on Optimization, 2013‏ - SIAM
We prove that any minimal valid function for the k-dimensional infinite group relaxation that
is continuous piecewise linear with at most k+1 slopes and does not factor through a linear …

The group-theoretic approach in mixed integer programming

JPP Richard, SS Dey - 50 Years of Integer Programming 1958-2008: From …, 2009‏ - Springer
In this chapter, we provide an overview of the mathematical foundations and recent
theoretical and computational advances in the study of the grouptheoretic approach in …

A geometric approach to cut-generating functions

A Basu, M Conforti, M Di Summa - Mathematical Programming, 2015‏ - Springer
The cutting-plane approach to integer programming was initiated more than 40 years ago:
Gomory introduced the corner polyhedron as a relaxation of a mixed integer set in tableau …

On degenerate multi-row Gomory cuts

G Zambelli - Operations Research Letters, 2009‏ - Elsevier
Borozan and Cornuéjols show that valid inequalities for an infinite relaxation for MIPs,
relative to some vertex f of the linear relaxation, are determined by maximal lattice-free …

Nonunique lifting of integer variables in minimal inequalities

A Basu, SS Dey, J Paat - SIAM Journal on Discrete Mathematics, 2019‏ - SIAM
We explore the lifting question in the context of cut-generating functions. Most of the prior
literature on this question focuses on cut-generating functions that have the unique lifting …