Gerard Cornuejols, professor, Carnegie Mellon University
and Universite d'Aix-Marseille.
Course Material
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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
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Combinatorial Optimization: Packing and Covering
Spring 2000. Published by SIAM (2001) in the CBMS-NSF 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).
The three conjectures in Chapter 9 were solved by Maria Chudnovsky
and Paul Seymour (2006).
Research Papers
1. Integer Programming
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On the Facets of Mixed Integer Programs with Two Integer Variables and Two Constraints by Gerard Cornuejols and
Francois Margot, August 2007.
To appear in Mathematical Programming A. (2008)
ps version
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Minimal Inequalities for Integer
Constraints by Valentin Borozan and Gerard Cornuejols, July 2007.
ps version
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A Feasibility Pump for Mixed Integer Nonlinear Programs
by Pierre Bonami, Gerard Cornuejols,
Andrea Lodi and Francois Margot, February 2006.
To appear in Mathematical Programming A. (2008)
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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, Published in
Discrete Optimization 5 (2008) 186-204.
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Valid Inequalities for Mixed Integer Linear Programs
by Gerard Cornuejols.
Published in Mathematical Programming B 112 (2008) 3-44.
ps version
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Projected Chvatal-Gomory Cuts for Mixed Integer Linear Programs
by Pierre Bonami, Gerard Cornuejols, Sanjeeb Dash, Matteo Fischetti
and Andrea Lodi.
Published in Mathematical Programming A 113 (2008) 241-257.
ps version
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A Note on the MIR Closure
by Pierre Bonami and Gerard Cornuejols.
Published in Operations Research Letters 36 (2008) 4-6.
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Revival of the Gomory Cuts in the 1990's
by Gerard Cornuejols.
Published in Annals of Operations Research
149 (2007) 63-66.
ps version
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Branching on General Disjunctions
by Miroslav Karamanov and Gerard Cornuejols,
July 2005.
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Early Estimates of the Size of Branch-and-Bound Trees
by Gerard Cornuejols, Miroslav Karamanov and Yanjun Li. Published in
INFORMS Journal on Computing 18 (2006) 86-96.
ps version
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A Convex-Analysis Perspective on Disjunctive Cuts
by Gerard Cornuejols and Claude Lemarechal,
Published in Mathematical Programming 106 (2006) 567-586.
ps version
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Reduce-and-Split Cuts: Improving the Performance of
Mixed Integer Gomory Cuts
by Kent Andersen, Gerard Cornuejols and Yanjun Li. Published in
Management Science 51 (2005) 1720-1732.
ps version
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Split Closure and Intersection Cuts
by Kent Andersen, Gerard Cornuejols and Yanjun Li. Published in
Mathematical Programming A 102 (2005) 457-493.
ps version
conference version
Published in IPCO 2002 (W.J. Cook and A.S. Schulz eds.),
Lecture Notes in Computer Science 2337 (2002) 127-144.
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K-Cuts: A Variation of Gomory Mixed
Integer Cuts from the LP Tableau
by Gerard Cornuejols, Yanjun Li and Dieter
Vandenbussche. Published in
INFORMS Journal on Computing 15 (2003) 385-396.
ps version
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A Connection Between Cutting Plane
Theory and the Geometry of Numbers
by Gerard Cornuejols and Yanjun Li. Published in
Mathematical Programming A 93 (2002) 123-127.
ps version
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On the Rank of Mixed 0,1
Polyhedra
by Gerard Cornuejols and Yanjun Li.
Published in Mathematical Programming A 91 (2002) 391-397.
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Elementary Closures for
Integer Programs
by Gerard Cornuejols and Yanjun Li.
Published in Operations Research Letters 28 (2001) 1-8.
2. Perfect Graphs
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Recognizing Berge Graphs
by Maria Chudnovsky, Gerard Cornuejols, Xinming Liu,
Paul Seymour and Kristina Vuskovic. Combinatorica
25 (2005) 143-186.
ps version
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Odd Hole Recognition in Graphs of Bounded Clique Size
by Michele Conforti, Gerard Cornuejols, Xinming Liu, Kristina Vuskovic
and Giacomo Zambelli. Published in
SIAM Journal on Discrete Mathematics 20 (2006) 42-48.
ps version
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The Strong Perfect Graph Theorem
by Gerard Cornuejols. Published in Optima 70 (2003) 2-6.
ps version .
French version: Seminaire Bourbaki
Le Theoreme Fort des Graphes
Parfaits. Published in Asterisque 311 (2007) 123-135.
ps version .
An earlier draft:
The Strong Perfect Graph Conjecture. Published in Proceedings of the
International Congress of Mathematicians III: Invited Lectures
Beijing (2002) 547-559. ps version
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Decomposing Berge Graphs Containing No Proper Wheel,
Long Prism or their Complements
by Michele Conforti, Gerard Cornuejols and Giacomo Zambelli.
Published in Combinatorica 26 (2006) 533-558.
ps version
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Decomposing Berge Graphs Containing Proper Wheels
by Michele Conforti, Gerard Cornuejols, Kristina Vuskovic
and Giacomo Zambelli, March 2002.
ps version
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Decomposition of Odd-Hole-Free Graphs by Double Star Cutsets and 2-Joins
by Michele Conforti, Gerard Cornuejols
and Kristina Vuskovic. Published in Discrete Mathematics
141 (2004) 41-91.
ps version
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Square-Free Perfect Graphs
by Michele Conforti, Gerard Cornuejols
and Kristina Vuskovic. Published in Journal of Combinatorial
Theory B 90 (2004) 257-307.
ps version
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A Class of Berge Graphs Containing P6
by Gerard Cornuejols and Xinming Liu. Published in
Journal of Combinatorial Theory B 87 (2003) 300-330.
ps version
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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. Published in
Journal of Combinatorial Theory B 87 (2003) 331-347.
ps version
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Perfect Graphs, Partitionable Graphs and Cutsets
by Michele Conforti, Gerard Cornuejols,
Grigor Gasparyan and Kristina Vuskovic.
Published in Combinatorica 22 (2002) 19-33.
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Even-Hole-Free Graphs Part I: Decomposition Theorem
by Michele Conforti, Gerard Cornuejols,
Ajai Kapoor and Kristina Vuskovic.
Published in Journal of Graph Theory 39 (2002) 6-49.
ps version
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Even-Hole-Free Graphs Part II: Recognition Algorithm
by Michele Conforti, Gerard Cornuejols,
Ajai Kapoor and Kristina Vuskovic.
Published in Journal of Graph Theory 40 (2002) 238-266.
ps version
3. Balanced Matrices
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Balanced Matrices
by Michele Conforti, Gerard Cornuejols and Kristina Vuskovic.
Published in Discrete Mathematics 306 (2006) 2411-2437.
ps version
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Bicolorings and Equitable Bicolorings of Matrices
by Michele Conforti, Gerard Cornuejols
and Giacomo Zambelli. Published in
MPS/SIAM Series on Optimization, The Sharpest Cut:
The Impact of Manfred Padberg and His Work ,
Martin Groetschel ed. (2004) 33-37.
ps version
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Decomposition of Balanced Matrices
by Michele Conforti, Gerard Cornuejols
and M. R. Rao. Published in Journal
of Combinatorial Theory B 77 (1999) 292-406.
Winner of the Fulkerson prize 2000, for best paper
in Discrete Mathematics (offered jointly by the Mathematical
Programming Society and the American Mathematical Society).
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Balanced 0+-1 Matrices Part I: Decomposition
by Michele Conforti, Gerard Cornuejols,
Ajai Kapoor and Kristina Vuskovic.
Published in Journal of Combinatorial Theory B 81
(2001) 243-274
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Balanced 0+-1 Matrices Part II: Recognition Algorithm
by Michele Conforti, Gerard Cornuejols,
Ajai Kapoor and Kristina Vuskovic.
Published in Journal of Combinatorial Theory B 81
(2001) 275-306
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On Padberg's Conjecture
about Almost Totally Unimodular Matrices
by Gerard Cornuejols and Luis F. Zuluaga. Published in
Operations Research Letters 27 (2000) 97-99.
4. Ideal Matrices
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Lehman Matrices
by Gerard Cornuejols, Bertrand Guenin and Levent Tuncel,
July 2006.
ps version
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Ideal Clutters
by Gerard Cornuejols and Bertrand Guenin. Published in
Discrete Applied Mathematics 123 (2002) 303-338.
ps version
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Ideal Binary Clutters, Connectivity
and a Conjecture of Seymour
by Gerard Cornuejols and Bertrand Guenin.
Published in SIAM Journal on Discrete Mathematics 15
(2002) 329-352.
ps version.
Winner of the SIAM Outstanding Paper Prize 2004.
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A Note on Dijoins
by Gerard Cornuejols and Bertrand Guenin.
Published in Discrete Mathematics 243 (2002)
213-216.
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The Packing Property
by Gerard Cornuejols, Bertrand Guenin and Francois Margot.
Published in Mathematical Programming A 89 (2000) 113-126.