**Gerard
Cornuejols, professor, Carnegie Mellon University. **

Course
Material

- Integer Programming 2014, by Michele Conforti, Gerard Cornuejols
and Giacomo Zambelli. Published by
*Springer.*http://www.springer.com/us/book/9783319110073 - Optimization Methods in Finance 2007, by Gerard Cornuejols and Reha Tutuncu. Published by
*Cambridge University Press.*

http://www.cambridge.org/us/academic/subjects/mathematics/mathematical-finance/optimization-methods-finance?format=HB - 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). 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 Lattice-Free Convex Sets
- Slides Lehman
Matrices

Research Papers

1. Integer Programming - On Some
Polytopes Contained in the 0,1 Hypercube that Have a Small
Chvatal Rank, by Gerard Cornuejols and Dabeen Lee, October 2015.
- Deciding Emptyness of the Gomory-Chvatal Closure in NP-Complete, Even for a Rational Polyhedron Containing No Integer Point, by Gerard Cornuejols and Yanjun Li, September 2015.
- Cut-Generating
Functions for Integer Variables, by Sercan Yildiz and Gerard Cornuejols,
December 2014, revised November 2015.
- Disjunctive Cuts for
Cross-Sections of the Second-Order Cone, by Sercan
Yildiz and Gerard Cornuejols.
*Operations Research Letters*43 (2015) 432-437. - 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.
*Mathematical Programming A*150 (2015) 459-489. - Sufficiency of
Cut-Generating Functions, by Gerard Cornuejols,
Laurence Wolsey and Sercan Yildiz.
*Mathematical Programming A*152 (2015) 643-651. - Cut-Generating Functions
and S-Free Sets, by Michele Conforti, Gerard
Cornuejols, Aris Daniilidis, Claude Lemarechal
and Jerome Malick.
*Mathematics of Operations Research*40 (2015) 276-301. - Cutting Planes from
Two-Term Disjunctions, by Pierre Bonami,
Michele Conforti, Gerard Cornuejols,
Marco Molinaro and Giacomo Zambelli.
*Operations Research Letters*41 (2013) 442-444. - On the Safety of Gomory Cut Generators, by Gerard Cornuejols, Francois Margot and Giacomo Nannicini.
*Mathematical Programming Computation*5 (2013) 345-395. - Lifting Gomory Cuts with Bounded Variables, by Gerard Cornuejols, Tamas Kis and Marco Molinaro.
*Operations Research Letters*41 (2013) 142-146. - Combining
Lift-and-Project and Reduce-and-Split, by Egon
Balas, Gerard Cornuejols,
Tamas Kis and Giacomo Nannicini.
*INFORMS Journal on Computing*25 (2013) 475-487. - A 3-Slope Theorem for
the Infinite Relaxation in the Plane, by Gerard Cornuejols
and Marco Molinaro.
*Mathematical Programming A*142 (2013) 83-105. - Extended
Formulations in Combinatorial Optimization, by Michele Conforti, Gerard Cornuejols
and Giacomo Zambelli.
*Annals of Operations Research*204 (2013) 97-143. An earlier draft appeared in*4OR - Quarterly Journal of Operations Research*8 (2010) 1-48. - 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) 109-121. - Intersection Cuts with
Infinite Split Rank, by Amitabh Basu, Gerard
Cornuejols and Francois Margot.
*Mathematics of Operations Research*37 (2012) 21-40. 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) 25-38. - Mixed Integer NonLinear Programs featuring "On/Off"
Constraints, by Hassan Hijazi, Pierre Bonami, Gerard Cornuejols
and Adam Ouorou.
*Computational Optimization and Applications*52 (2012) 537-558. - Unique
Minimal Liftings for Simplicial Polytopes, by
Amitabh Basu, Gerard Cornuejols
and Matthias Koeppe.
*Mathematics of Operations Research*37 (2012) 346-355. - 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) 561-576. IPCO version: On Lifting Integer Variables in Minimal Inequalities, IPCO 2010, Lausanne,*LNCS 6080*(2010) 85-95. - A Geometric
Perspective on Lifting, by Michele Conforti,
Gerard Cornuejols and Giacomo Zambelli.
*Operations Research*59 (2011) 569-577. - Corner
Polyhedron and Intersection Cuts, by Michele Conforti,
Gerard Cornuejols and Giacomo Zambelli.
*Surveys in Operations Research and Management Science*16 (2011) 105-120. - Practical Strategies for
Generating Rank-1 Split Cuts in Mixed-Integer Linear Programming, by
Gerard Cornuejols and Giacomo Nannicini.
*Mathematical Programming Computation*3 (2011) 281-318. - Experiments
with Two-Row Cuts from Degenerate Tableaux, by Amitabh Basu, Pierre Bonami, Gerard Cornuejols and Francois Margot.
*INFORMS Journal on Computing*23 (2011) 578-590. - Improved Strategies for
Branching on General Disjunctions, by Gerard Cornuejols,
Leo Liberti and Giacomo Nannicini.
*Mathematical Programming A*130 (2011) 225-247. 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) 164-182. - Branching on
General Disjunctions, by Miroslav Karamanov
and Gerard Cornuejols. ps
version 2005.
*Mathematical Programming A*128 (2011) 403-436. - 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) 27-38. - 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) 281-314. Conference version in SODA 2009, 1220-1229. - Convex Sets
and Minimal Sublinear Functions, by Amitabh Basu,
Gerard Cornuejols and Giacomo Zambelli.
*Journal of Convex Analysis*18 (2011) 427-432. 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) 158-168. - Maximal
Lattice-free Convex Sets in Linear Subspaces, by Amitabh Basu, Michele Conforti,
Gerard Cornuejols and Giacomo Zambelli.
*Mathematics of Operations Research*35 (2010) 704-720. - Equivalence between
Intersection Cuts and the Corner Polyhedron, by Michele Conforti, Gerard Cornuejols
and Giacomo Zambelli.
*Operations Research Letters*38 (2010) 153-155. - Stable Sets,
Corner Polyhedra and the Chvatal
Closure, by Manoel Campelo
and Gerard Cornuejols.
*Operations Research Letters*37 (2009) 375-378. 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) 429-456. ps version. Conference version in LATIN 2008, 317-328. - Minimal
Valid Inequalities for Integer Constraints, by Valentin Borozan and Gerard Cornuejols.
*Mathematics of Operations Research*34 (2009) 538-546. 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) 343-386. 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) 331-352. - 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) 186-204. The most frequently cited paper published in*Discrete Optimization*2005-2010. - Valid
Inequalities for Mixed Integer Linear Programs, by Gerard Cornuejols.
*Mathematical Programming B*112 (2008) 3-44. ps version - Projected Chvatal-Gomory Cuts for Mixed Integer Linear Programs,
by Pierre Bonami, Gerard Cornuejols,
Sanjeeb Dash, Matteo Fischetti
and Andrea Lodi.
*Mathematical Programming A*113 (2008) 241-257. ps version - A Note on the MIR
Closure, by Pierre Bonami and Gerard Cornuejols.
*Operations Research Letters*36 (2008) 4-6. - Revival of the Gomory Cuts in the 1990's, by Gerard Cornuejols.
*Annals of Operations Research*149 (2007) 63-66. ps version - Early Estimates of
the Size of Branch-and-Bound Trees, by Gerard Cornuejols,
Miroslav Karamanov and Yanjun
Li.
*INFORMS Journal on Computing*18 (2006) 86-96. ps version - A Convex-Analysis Perspective
on Disjunctive Cuts, by Gerard Cornuejols
and Claude Lemarechal,
*Mathematical Programming A*106 (2006) 567-586. ps version - Reduce-and-Split Cuts:
Improving the Performance of Mixed Integer Gomory
Cuts, by Kent Andersen, Gerard Cornuejols
and Yanjun Li.
*Management Science*51 (2005) 1720-1732. ps version - Split Closure and
Intersection Cuts, by Kent Andersen, Gerard Cornuejols
and Yanjun Li.
*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. - K-Cuts: 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) 385-396. ps version - A Connection Between
Cutting Plane Theory and the Geometry of Numbers, by Gerard Cornuejols and Yanjun Li.
*Mathematical Programming A*93 (2002) 123-127. ps version - On the Rank of Mixed 0,1 Polyhedra, by Gerard Cornuejols and Yanjun Li.
*Mathematical Programming A*91 (2002) 391-397. - Elementary Closures for
Integer Programs, by Gerard Cornuejols and Yanjun Li.
*Operations Research Letters*28 (2001) 1-8.

2. Perfect Graphs - Recognizing Berge Graphs,
by Maria Chudnovsky, Gerard Cornuejols, Xinming Liu,
Paul Seymour and Kristina Vuskovic.
*Combinatorica* - 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) 42-48. ps version - The Strong Perfect Graph
Theorem, by Gerard Cornuejols.
*Optima*70 (2003) 2-6. ps version . French version: Seminaire Bourbaki Le Theoreme Fort des Graphes Parfaits. Published in*Asterisque**Proceedings of the International Congress of Mathematicians III: Invited Lectures*Beijing (2002) 547-559. ps version - Decomposing Berge Graphs
Containing No Proper Wheel, Long Prism or their Complements, by
Michele Conforti, Gerard Cornuejols
and Giacomo Zambelli.
*Combinatorica* - Decomposing Berge
Graphs Containing Proper Wheels, by Michele Conforti,
Gerard Cornuejols, Kristina Vuskovic
and Giacomo Zambelli, March 2002. ps version
- Decomposition of
Odd-Hole-Free Graphs by Double Star Cutsets and
2-Joins, by Michele Conforti, Gerard Cornuejols and Kristina Vuskovic.
*Discrete Mathematics*141 (2004) 41-91. ps version - Square-Free Perfect
Graphs, by Michele Conforti, Gerard Cornuejols and Kristina Vuskovic.
*Journal of Combinatorial Theory B*90 (2004) 257-307. ps version - A Class of Berge Graphs
Containing P6, by Gerard Cornuejols and Xinming Liu.
*Journal of Combinatorial Theory B*87 (2003) 300-330. 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) 331-347. ps version - Perfect Graphs, Partitionable Graphs and Cutsets,
by Michele Conforti, Gerard Cornuejols, Grigor Gasparyan
and Kristina Vuskovic.
*Combinatorica* - Even-Hole-Free Graphs
Part I: Decomposition Theorem, by Michele Conforti,
Gerard Cornuejols, Ajai
Kapoor and Kristina Vuskovic.
*Journal of Graph Theory*39 (2002) 6-49. ps version - Even-Hole-Free Graphs
Part II: Recognition Algorithm, by Michele Conforti,
Gerard Cornuejols, Ajai
Kapoor and Kristina Vuskovic.
*Journal of Graph Theory*40 (2002) 238-266. ps version

3. Balanced Matrices - Balanced Matrices, by
Michele Conforti, Gerard Cornuejols
and Kristina Vuskovic.
*Discrete Mathematics*306 (2006) 2411-2437. 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) 33-37. ps version - Decomposition of Balanced
Matrices, by Michele Conforti, Gerard Cornuejols and M. R. Rao.
*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). - Balanced 0+-1 Matrices
Part I: Decomposition, by Michele Conforti,
Gerard Cornuejols, Ajai
Kapoor and Kristina Vuskovic.
*Journal of Combinatorial Theory B*81 (2001) 243-274 - 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) 275-306 - On Padberg's
Conjecture about Almost Totally Unimodular
Matrices, by Gerard Cornuejols and Luis F. Zuluaga.
*Operations Research Letters*27 (2000) 97-99.

4. Ideal Matrices - Lehman Matrices, by
Gerard Cornuejols, Bertrand Guenin
and Levent Tuncel.
*Journal of Combinatorial Theory B*99 (2009) 531-556. DOI 10.1016/j.jctb.2008.06.009 ps version - Ideal Clutters, by
Gerard Cornuejols and Bertrand Guenin.
*Discrete Applied Mathematics*123 (2002) 303-338. ps version - Ideal Binary Clutters,
Connectivity and a Conjecture of Seymour, by Gerard Cornuejols and Bertrand Guenin.
*SIAM Journal on Discrete Mathematics*15 (2002) 329-352. ps version. Winner of the SIAM Outstanding Paper Prize 2004. - A Note on Dijoins, by Gerard Cornuejols
and Bertrand Guenin.
*Discrete Mathematics*243 (2002) 213-216. - The Packing Property, by
Gerard Cornuejols, Bertrand Guenin
and Francois Margot.
*Mathematical Programming A*89 (2000) 113-126.