Gerard Cornuejols, professor, Carnegie Mellon University and Universite d'Aix-Marseille.

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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 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
  
• 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
  
• Minimal Inequalities for Integer Constraints by Valentin Borozan and Gerard Cornuejols, July 2007. ps version
  
• 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)
  
• 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.
  
• Valid Inequalities for Mixed Integer Linear Programs by Gerard Cornuejols. Published in 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. Published in Mathematical Programming A 113 (2008) 241-257. ps version
  
• A Note on the MIR Closure by Pierre Bonami and Gerard Cornuejols. Published in Operations Research Letters 36 (2008) 4-6.
  
• Revival of the Gomory Cuts in the 1990's by Gerard Cornuejols. Published in Annals of Operations Research 149 (2007) 63-66. ps version
  
• Branching on General Disjunctions by Miroslav Karamanov and Gerard Cornuejols, July 2005.
  
• 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
  
• A Convex-Analysis Perspective on Disjunctive Cuts by Gerard Cornuejols and Claude Lemarechal, Published in Mathematical Programming 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. Published in Management Science 51 (2005) 1720-1732. ps version
  
• 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.
  
• 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
  
• 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
  
• On the Rank of Mixed 0,1 Polyhedra by Gerard Cornuejols and Yanjun Li. Published in Mathematical Programming A 91 (2002) 391-397.
  
• Elementary Closures for Integer Programs by Gerard Cornuejols and Yanjun Li. Published in 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 25 (2005) 143-186. ps version
  
• 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
  
• 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
  
• 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
  
• 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. Published in Discrete Mathematics 141 (2004) 41-91. ps version
  
• 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
  
• 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
  
• 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
  
• Perfect Graphs, Partitionable Graphs and Cutsets by Michele Conforti, Gerard Cornuejols, Grigor Gasparyan and Kristina Vuskovic. Published in Combinatorica 22 (2002) 19-33.
  
• 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
  
• 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
  
• Balanced Matrices by Michele Conforti, Gerard Cornuejols and Kristina Vuskovic. Published in Discrete Mathematics 306 (2006) 2411-2437. ps version
  
• 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
  
• 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).
  
• 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
  
• 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
  
• 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
  
• Lehman Matrices by Gerard Cornuejols, Bertrand Guenin and Levent Tuncel, July 2006. ps version
  
• Ideal Clutters by Gerard Cornuejols and Bertrand Guenin. Published in Discrete Applied Mathematics 123 (2002) 303-338. ps version
  
• 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.
  
• A Note on Dijoins by Gerard Cornuejols and Bertrand Guenin. Published in Discrete Mathematics 243 (2002) 213-216.
  
• The Packing Property by Gerard Cornuejols, Bertrand Guenin and Francois Margot. Published in Mathematical Programming A 89 (2000) 113-126.