Gerard Cornuejols, professor, Carnegie Mellon University.
Course Material

Optimization Methods in Finance 2007, by Gerard Cornuejols and Reha Tutuncu. Published by Cambridge University Press.
http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=9780521861700

Combinatorial Optimization: Packing and Covering Spring 2000. Published by SIAM (2001) in the CBMSNSF Regional Conference Series in Applied Mathematics
CBMS 74. ps version
The two conjectures in Chapter 3 were solved by Maria Chudnovsky, Robin Thomas, Neil Robertson and Paul Seymour (2002). Conjecture 4.14
in Chapter 4 was solved by Jonathan Wang (2010). The three conjectures in Chapter 9 were solved by Maria Chudnovsky and Paul Seymour (2006). Twelve are still unsolved!

Slides Cut Generating Functions

Slides A Geometric View on Integer Lifting

Slides Corner Polyhedron, Intersection Cuts and Maximal
LatticeFree Convex Sets

Slides Lehman Matrices
Research Papers
1. Integer Programming

On the Relative Strength of Families of Intersection Cuts Arising from Pairs of Tableau Constraints
in Mixed Integer Programs,
by Yogesh Awate, Gerard Cornuejols, Bertrand Guenin and Levent Tuncel, March 2013, revised March 2014. To appear in Mathematical Programming A .
DOI 10.1007/s101070140775z

Sufficiency of CutGenerating Functions,
by Gerard Cornuejols, Laurence Wolsey and Sercan Yildiz, April 2013, revised December 2013. To appear in Mathematical Programming A .
DOI 10.1007/s1010701407802

CutGenerating Functions and SFree Sets,
by Michele Conforti, Gerard Cornuejols, Aris Daniilidis, Claude Lemarechal and Jerome Malick, February 2013, revised March 2014.
To appear in Mathematics of Operations Research .

Cutting Planes from TwoTerm Disjunctions,
by Pierre Bonami, Michele Conforti, Gerard Cornuejols, Marco Molinaro and Giacomo Zambelli.
Operations Research Letters 41 (2013) 442444.

On the Safety of Gomory Cut Generators,
by Gerard Cornuejols, Francois Margot and Giacomo Nannicini.
Mathematical Programming Computation 5 (2013) 345395.

Lifting Gomory Cuts with Bounded Variables,
by Gerard Cornuejols, Tamas Kis and Marco Molinaro.
Operations Research Letters 41 (2013) 142146.

Combining LiftandProject and ReduceandSplit,
by Egon Balas, Gerard Cornuejols, Tamas Kis and Giacomo Nannicini.
INFORMS Journal on Computing 25 (2013) 475487.

A 3Slope Theorem for the Infinite Relaxation in the Plane,
by Gerard Cornuejols and Marco Molinaro.
Mathematical Programming A 142 (2013) 83105.
 Extended Formulations in
Combinatorial Optimization,
by Michele Conforti, Gerard Cornuejols and Giacomo Zambelli.
Annals of Operations Research 204 (2013) 97143.
An earlier draft appeared in
4OR  Quarterly Journal of Operations Research 8 (2010) 148.

How Tight is the Corner Relaxation? Insights Gained from the Stable Set Problem
by Gerard Cornuejols, Carla Michini and Giacomo Nannicini.
Discrete Optimization 9 (2012) 109121.

Intersection Cuts with Infinite Split Rank,
by Amitabh Basu, Gerard Cornuejols and Francois Margot.
Mathematics of Operations Research 37 (2012) 2140. Erratum

A Counterexample to a Conjecture of Gomory and Johnson,
by Amitabh Basu, Michele Conforti, Gerard Cornuejols and Giacomo Zambelli.
Mathematical Programming A 133 (2012) 2538.

Mixed Integer NonLinear Programs featuring "On/Off" Constraints,
by Hassan Hijazi, Pierre Bonami, Gerard Cornuejols and Adam Ouorou.
Computational Optimization and Applications 52 (2012) 537558.

Unique Minimal Liftings for Simplicial Polytopes,
by Amitabh Basu, Gerard Cornuejols and Matthias Koeppe. Mathematics of Operations Research 37 (2012)
346355.

Unique Lifting of Integer Variables
in Minimal Inequalities, by Amitabh Basu, Manoel Campelo, Michele Conforti, Gerard Cornuejols
and Giacomo Zambelli. Mathematical Programming A 141 (2013) 561576.
IPCO version:
On Lifting Integer Variables in Minimal Inequalities,
IPCO 2010, Lausanne, LNCS 6080 (2010) 8595.

A Geometric Perspective on Lifting,
by Michele Conforti, Gerard Cornuejols and Giacomo Zambelli.
Operations Research 59 (2011) 569577.

Corner Polyhedron and Intersection Cuts,
by Michele Conforti, Gerard Cornuejols and Giacomo Zambelli.
Surveys in Operations Research and Management Science 16 (2011) 105120.

Practical Strategies for Generating Rank1 Split Cuts
in MixedInteger Linear Programming,
by Gerard Cornuejols and Giacomo Nannicini.
Mathematical Programming Computation 3 (2011) 281318.

Experiments with TwoRow Cuts from Degenerate Tableaux,
by Amitabh Basu, Pierre Bonami, Gerard Cornuejols and Francois Margot.
INFORMS Journal on Computing 23 (2011) 578590.

Improved Strategies for Branching on General Disjunctions,
by Gerard Cornuejols, Leo Liberti and Giacomo Nannicini.
Mathematical Programming A 130 (2011) 225247.
Related paper: Branching on Split Disjunctions
by Giacomo Nannicini, Gerard Cornuejols, Miroslav Karamanov and Leo Liberti, in
Combinatorial Optimization: Methods and Applications, V. Chvatal ed., IOS Press (2011) 164182.

Branching on General Disjunctions,
by Miroslav Karamanov and Gerard Cornuejols. ps version 2005.
Mathematical Programming A 128 (2011) 403436.

A Probabilistic Analysis of the Strength of the
Split and Triangle Closures,
by Amitabh Basu, Gerard Cornuejols and Marco Molinaro, October 2010.
IPCO 2011 version , O. Günlük and G. J. Woeginger eds., LNCS 6655 (2011) 2738.

On the Relative Strength of Split, Triangle and Quadrilateral Cuts,
by Amitabh Basu, Pierre Bonami, Gerard Cornuejols and Francois Margot.
Mathematical Programming A 126 (2011) 281314. Conference version in SODA 2009, 12201229.

Convex Sets and Minimal Sublinear Functions,
by Amitabh Basu, Gerard Cornuejols and Giacomo Zambelli.
Journal of Convex Analysis 18 (2011) 427432.
ps version

Minimal Inequalities for an Infinite Relaxation of Integer Programs,
by Amitabh Basu, Michele Conforti, Gerard Cornuejols and Giacomo Zambelli.
SIAM Journal on Discrete Mathematics 24 (2010) 158168.

Maximal Latticefree Convex Sets in Linear Subspaces,
by Amitabh Basu, Michele Conforti, Gerard Cornuejols and Giacomo Zambelli.
Mathematics of Operations Research 35 (2010) 704720.

Equivalence between Intersection Cuts and the Corner
Polyhedron, by Michele Conforti, Gerard Cornuejols and Giacomo Zambelli.
Operations Research Letters 38 (2010) 153155.

Stable Sets, Corner Polyhedra and the Chvatal Closure,
by Manoel Campelo and Gerard Cornuejols. Operations Research Letters 37 (2009) 375378.
previous version

On the Facets of Mixed Integer Programs with Two Integer Variables
and Two Constraints,
by Gerard Cornuejols and Francois Margot. Mathematical Programming A 120 (2009) 429456.
ps version. Conference version in LATIN 2008, 317328.

Minimal Valid Inequalities for Integer
Constraints, by Valentin Borozan and Gerard Cornuejols.
Mathematics of Operations Research 34 (2009) 538546.
ps version

Polyhedral Approaches to Mixed Integer Linear Programming,
by Michele Conforti, Gerard Cornuejols and Giacomo Zambelli.
50 Years of Integer Programming edited by Michael Juenger, Springer Verlag (2009) 343386.
ps version

A Feasibility Pump for Mixed Integer Nonlinear Programs,
by Pierre Bonami, Gerard Cornuejols, Andrea Lodi and Francois Margot.
Mathematical Programming A 119 (2009) 331352.

An Algorithmic Framework for Convex Mixed Integer Nonlinear Programs,
by Pierre Bonami, Andreas Waechter, Lorenz Biegler, Andrew Conn,
Gerard Cornuejols, Ignacio Grossmann, Carl Laird, Jon Lee,
Andrea Lodi, Francois Margot and Nicolas Sawaya.
Discrete Optimization 5 (2008) 186204. The most frequently cited paper published in
Discrete Optimization 20052010.

Valid Inequalities for Mixed Integer Linear Programs,
by Gerard Cornuejols.
Mathematical Programming B 112 (2008) 344.
ps version

Projected ChvatalGomory Cuts for Mixed Integer Linear Programs,
by Pierre Bonami, Gerard Cornuejols, Sanjeeb Dash, Matteo Fischetti
and Andrea Lodi.
Mathematical Programming A 113 (2008) 241257.
ps version

A Note on the MIR Closure,
by Pierre Bonami and Gerard Cornuejols.
Operations Research Letters 36 (2008) 46.

Revival of the Gomory Cuts in the 1990's,
by Gerard Cornuejols.
Annals of Operations Research
149 (2007) 6366.
ps version

Early Estimates of the Size of BranchandBound Trees,
by Gerard Cornuejols, Miroslav Karamanov and Yanjun Li.
INFORMS Journal on Computing 18 (2006) 8696.
ps version

A ConvexAnalysis Perspective on Disjunctive Cuts,
by Gerard Cornuejols and Claude Lemarechal,
Mathematical Programming A 106 (2006) 567586.
ps version

ReduceandSplit Cuts: Improving the Performance of
Mixed Integer Gomory Cuts,
by Kent Andersen, Gerard Cornuejols and Yanjun Li.
Management Science 51 (2005) 17201732.
ps version

Split Closure and Intersection Cuts,
by Kent Andersen, Gerard Cornuejols and Yanjun Li.
Mathematical Programming A 102 (2005) 457493.
ps version
conference version
Published in IPCO 2002 (W.J. Cook and A.S. Schulz eds.),
Lecture Notes in Computer Science 2337 (2002) 127144.

KCuts: A Variation of Gomory Mixed
Integer Cuts from the LP Tableau,
by Gerard Cornuejols, Yanjun Li and Dieter
Vandenbussche.
INFORMS Journal on Computing 15 (2003) 385396.
ps version

A Connection Between Cutting Plane
Theory and the Geometry of Numbers,
by Gerard Cornuejols and Yanjun Li.
Mathematical Programming A 93 (2002) 123127.
ps version

On the Rank of Mixed 0,1
Polyhedra,
by Gerard Cornuejols and Yanjun Li.
Mathematical Programming A 91 (2002) 391397.

Elementary Closures for
Integer Programs,
by Gerard Cornuejols and Yanjun Li.
Operations Research Letters 28 (2001) 18.
2. Perfect Graphs

Recognizing Berge Graphs,
by Maria Chudnovsky, Gerard Cornuejols, Xinming Liu,
Paul Seymour and Kristina Vuskovic. Combinatorica
25 (2005) 143186.
ps version

Odd Hole Recognition in Graphs of Bounded Clique Size,
by Michele Conforti, Gerard Cornuejols, Xinming Liu, Kristina Vuskovic
and Giacomo Zambelli.
SIAM Journal on Discrete Mathematics 20 (2006) 4248.
ps version

The Strong Perfect Graph Theorem,
by Gerard Cornuejols. Optima 70 (2003) 26.
ps version .
French version: Seminaire Bourbaki
Le Theoreme Fort des Graphes
Parfaits. Published in Asterisque 311 (2007) 123135.
ps version .
An earlier draft:
The Strong Perfect Graph Conjecture. Proceedings of the
International Congress of Mathematicians III: Invited Lectures
Beijing (2002) 547559. ps version

Decomposing Berge Graphs Containing No Proper Wheel,
Long Prism or their Complements,
by Michele Conforti, Gerard Cornuejols and Giacomo Zambelli.
Combinatorica 26 (2006) 533558.
ps version

Decomposing Berge Graphs Containing Proper Wheels,
by Michele Conforti, Gerard Cornuejols, Kristina Vuskovic
and Giacomo Zambelli, March 2002.
ps version

Decomposition of OddHoleFree Graphs by Double Star Cutsets and 2Joins,
by Michele Conforti, Gerard Cornuejols
and Kristina Vuskovic. Discrete Mathematics
141 (2004) 4191.
ps version

SquareFree Perfect Graphs,
by Michele Conforti, Gerard Cornuejols
and Kristina Vuskovic. Journal of Combinatorial
Theory B 90 (2004) 257307.
ps version

A Class of Berge Graphs Containing P6,
by Gerard Cornuejols and Xinming Liu.
Journal of Combinatorial Theory B 87 (2003) 300330.
ps version

Graphs without Odd Holes, Parachutes or Proper Wheels:
A Generalization of Meyniel Graphs and of Line Graphs
of Bipartite Graphs,
by Michele Conforti, Gerard Cornuejols.
Journal of Combinatorial Theory B 87 (2003) 331347.
ps version

Perfect Graphs, Partitionable Graphs and Cutsets,
by Michele Conforti, Gerard Cornuejols,
Grigor Gasparyan and Kristina Vuskovic.
Combinatorica 22 (2002) 1933.

EvenHoleFree Graphs Part I: Decomposition Theorem,
by Michele Conforti, Gerard Cornuejols,
Ajai Kapoor and Kristina Vuskovic.
Journal of Graph Theory 39 (2002) 649.
ps version

EvenHoleFree Graphs Part II: Recognition Algorithm,
by Michele Conforti, Gerard Cornuejols,
Ajai Kapoor and Kristina Vuskovic.
Journal of Graph Theory 40 (2002) 238266.
ps version
3. Balanced Matrices

Balanced Matrices,
by Michele Conforti, Gerard Cornuejols and Kristina Vuskovic.
Discrete Mathematics 306 (2006) 24112437.
ps version

Bicolorings and Equitable Bicolorings of Matrices,
by Michele Conforti, Gerard Cornuejols
and Giacomo Zambelli.
MPS/SIAM Series on Optimization, The Sharpest Cut:
The Impact of Manfred Padberg and His Work ,
Martin Groetschel ed. (2004) 3337.
ps version

Decomposition of Balanced Matrices,
by Michele Conforti, Gerard Cornuejols
and M. R. Rao. Journal
of Combinatorial Theory B 77 (1999) 292406.
Winner of the Fulkerson prize 2000, for best paper
in Discrete Mathematics (offered jointly by the Mathematical
Programming Society and the American Mathematical Society).

Balanced 0+1 Matrices Part I: Decomposition,
by Michele Conforti, Gerard Cornuejols,
Ajai Kapoor and Kristina Vuskovic.
Journal of Combinatorial Theory B 81
(2001) 243274

Balanced 0+1 Matrices Part II: Recognition Algorithm,
by Michele Conforti, Gerard Cornuejols,
Ajai Kapoor and Kristina Vuskovic.
Journal of Combinatorial Theory B 81
(2001) 275306

On Padberg's Conjecture
about Almost Totally Unimodular Matrices,
by Gerard Cornuejols and Luis F. Zuluaga.
Operations Research Letters 27 (2000) 9799.
4. Ideal Matrices

Lehman Matrices,
by Gerard Cornuejols, Bertrand Guenin and Levent Tuncel.
Journal of Combinatorial Theory B 99 (2009) 531556.
DOI 10.1016/j.jctb.2008.06.009
ps version

Ideal Clutters,
by Gerard Cornuejols and Bertrand Guenin.
Discrete Applied Mathematics 123 (2002) 303338.
ps version

Ideal Binary Clutters, Connectivity
and a Conjecture of Seymour,
by Gerard Cornuejols and Bertrand Guenin.
SIAM Journal on Discrete Mathematics 15
(2002) 329352.
ps version.
Winner of the SIAM Outstanding Paper Prize 2004.

A Note on Dijoins,
by Gerard Cornuejols and Bertrand Guenin.
Discrete Mathematics 243 (2002)
213216.

The Packing Property,
by Gerard Cornuejols, Bertrand Guenin and Francois Margot.
Mathematical Programming A 89 (2000) 113126.