Grard Cornujols

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Found 26 papers in total

Cut-Generating Functions for Integer Variables

2016

For an integer linear program, Gomory’s corner relaxation is obtained by...

Combining Lift‐and‐Project and Reduce‐and‐Split

2013

Split cuts constitute a class of cutting planes that has been successfully employed by...

Extended formulations in combinatorial optimization

2013

This survey is concerned with the size of perfect formulations for combinatorial...

Intersection Cuts with Infinite Split Rank

2012

We consider mixed‐integer linear programs where free integer variables are...

How tight is the corner relaxation? Insights gained from the stable set problem

2012

The corner relaxation of a mixed‐integer linear program is a central concept in...

Experiments with Two‐Row Cuts from Degenerate Tableaux

2011

There has been a recent interest in cutting planes generated from two or more rows of...

A Geometric Perspective on Lifting

2011

Recently it has been shown that minimal inequalities for a continuous relaxation of...

Maximal lattice-free convex sets in linear subspaces

2010

We consider a model that arises in integer programming and show that all irredundant...

A note on the MIR closure

2008

In 1988, Nemhauser and Wolsey introduced the concept of mixed integer rounding (MIR)...

An algorithmic framework for convex mixed integer nonlinear programs

2008

This paper is motivated by the fact that mixed integer nonlinear programming is an...

A note on the mixed-integer rounding (MIR) closure

2008

In 1988, Nemhauser and Wolsey introduced the concept of MIR inequality for mixed...

Reduce-and-split cuts: improving the performance of mixed-integer Gomory cuts

2005

Mixed-integer Gomory cuts have become an integral part of state-of-the-art software...

Revival of the Gomory cuts in the 1990's

2007

This paper is one in a special issue of Annals of Operations Research devoted to the...

Early estimates of the size of branch-and-bound trees

2006

This paper intends to show that the time needed to solve mixed-integer-programming...

K-cuts: A variation of Gomory mixed integer cuts from the LP tableau

2003

For an integer program, a k -cut is a cutting plane generated by the Gomory mixed...

On Padberg's conjecture about almost totally unimodular matrices

2000

We consider Padberg's conjecture about almost totally unimodular matrices proposed in...

Perfect, ideal and balanced matrices

2001

In this paper, we survey results and open problems on perfect, ideal and balanced...

Elementary closures for integer programs

2001

In integer programming, the elementary closure associated with a family of cuts is the...

A class of hard small 0–1 programs

1999

In this article, we consider a class of 0–1 programs that, although innocent...

Mixed 0–1 programming by lift-and-project in a branch-and-cut framework

1996

We investigate the computational issues that need to be addressed when incorporating...

Balanced 0, ¸ℝà1-matrices, bicoloring and total dual integrality

1995

A 0,¸±1-matrix A is balanced if, in every submatrix with two nonzero...

A lift-and-project cutting plane algorithm for mixed 0-1 programming problems

1993

The authors propose a cutting plane algorithm for mixed 0-1 programs based on a family...

Polyhedral study of the capacitated vehicle routing problem

1993

The capacitated vehicle routing problem (CVRP) considered in this paper occurs when...

From totally unimodular to balanced

1994

In this paper the authors introduce a family of integer polytopes and characterize...

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