Integer Programming |
Packing and Covering |
Optimality certificates for convex minimization and Helly numbers, by Amitabh Basu, Michele Conforti, Gerard Cornuejols, Robert Weismantel and Stefan Weltge, October 2016. | Ideal clutters that do not pack, by Ahmad Abdi, Gerard Cornuejols and Kanstantsin Pashkovich, September 2016. |
Recognizing Berge Graphs, by Maria Chudnovsky, Gerard Cornuejols, Xinming Liu, Paul Seymour and Kristina Vuskovic. Combinatorica 25 (2005) 143-186. ps version | |
On Some Polytopes Contained in the 0,1 Hypercube that Have a Small Chvatal Rank, by Gerard Cornuejols and Dabeen Lee, October 2015. | 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 |
When the Gomory-Chvatal Closure Coincides with the Integer Hull, by Gerard Cornuejols and Yanjun Li, March 2016. IPCO version: Deciding Emptyness of the Gomory-Chvatal Closure is NP-Complete, Even for a Rational Polyhedron Containing No Integer Point. | 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 311 (2007) 123-135. ps version. An earlier draft: The Strong Perfect Graph Conjecture. Proceedings of the International Congress of Mathematicians III: Invited Lectures Beijing (2002) 547-559. ps version |
Cut-Generating Functions for Integer Variables, by Sercan Yildiz and Gerard Cornuejols, Mathematics of Operations Research 41 (2016) 1381-1403. | Decomposing Berge Graphs Containing No Proper Wheel, Long Prism or their Complements, by Michele Conforti, Gerard Cornuejols and Giacomo Zambelli. Combinatorica 26 (2006) 533-558. ps version |
Disjunctive Cuts for Cross-Sections of the Second-Order Cone, by Sercan Yildiz and Gerard Cornuejols. Operations Research Letters 43 (2015) 432-437. | Decomposing Berge Graphs Containing Proper Wheels, by Michele Conforti, Gerard Cornuejols, Kristina Vuskovic and Giacomo Zambelli, March 2002. ps version |
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. | 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 |
Sufficiency of Cut-Generating Functions, by Gerard Cornuejols, Laurence Wolsey and Sercan Yildiz. Mathematical Programming A 152 (2015) 643-651. | Square-Free Perfect Graphs, by Michele Conforti, Gerard Cornuejols and Kristina Vuskovic. Journal of Combinatorial Theory B 90 (2004) 257-307. ps version |
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. | A Class of Berge Graphs Containing P6, by Gerard Cornuejols and Xinming Liu. Journal of Combinatorial Theory B 87 (2003) 300-330. ps version |
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. | 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 |
On the Safety of Gomory Cut Generators, by Gerard Cornuejols, Francois Margot and Giacomo Nannicini. Mathematical Programming Computation 5 (2013) 345-395. | Perfect Graphs, Partitionable Graphs and Cutsets, by Michele Conforti, Gerard Cornuejols, Grigor Gasparyan and Kristina Vuskovic. Combinatorica 22 (2002) 19-33. |
Lifting Gomory Cuts with Bounded Variables, by Gerard Cornuejols, Tamas Kis and Marco Molinaro. Operations Research Letters 41 (2013) 142-146. | 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 |
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. | 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 |
A 3-Slope Theorem for the Infinite Relaxation in the Plane, by Gerard Cornuejols and Marco Molinaro. Mathematical Programming A 142 (2013) 83-105. | Balanced Matrices, by Michele Conforti, Gerard Cornuejols and Kristina Vuskovic. Discrete Mathematics 306 (2006) 2411-2437. ps version |
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. | 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 |
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. | 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). |
Intersection Cuts with Infinite Split Rank, by Amitabh Basu, Gerard Cornuejols and Francois Margot. Mathematics of Operations Research 37 (2012) 21-40. Erratum | 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 |
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. | 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 |
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. | 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 |
Unique Minimal Liftings for Simplicial Polytopes, by Amitabh Basu, Gerard Cornuejols and Matthias Koeppe. Mathematics of Operations Research 37 (2012) 346-355. | 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 |
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. | Ideal Clutters, by Gerard Cornuejols and Bertrand Guenin. Discrete Applied Mathematics 123 (2002) 303-338. ps version |
A Geometric Perspective on Lifting, by Michele Conforti, Gerard Cornuejols and Giacomo Zambelli. Operations Research 59 (2011) 569-577. | 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. |
Corner Polyhedron and Intersection Cuts, by Michele Conforti, Gerard Cornuejols and Giacomo Zambelli. Surveys in Operations Research and Management Science 16 (2011) 105-120. | A Note on Dijoins, by Gerard Cornuejols and Bertrand Guenin. Discrete Mathematics 243 (2002) 213-216. |
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. | The Packing Property, by Gerard Cornuejols, Bertrand Guenin and Francois Margot. Mathematical Programming A 89 (2000) 113-126. |
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. | Recognizing Berge Graphs, by Maria Chudnovsky, Gerard Cornuejols, Xinming Liu, Paul Seymour and Kristina Vuskovic. Combinatorica 25 (2005) 143-186. ps version |
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. | 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 |
Branching on General Disjunctions, by Miroslav Karamanov and Gerard Cornuejols. ps version 2005. Mathematical Programming A 128 (2011) 403-436. | 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 311 (2007) 123-135. ps version. An earlier draft: The Strong Perfect Graph Conjecture. Proceedings of the International Congress of Mathematicians III: Invited Lectures Beijing (2002) 547-559. ps version |
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. | Decomposing Berge Graphs Containing No Proper Wheel, Long Prism or their Complements, by Michele Conforti, Gerard Cornuejols and Giacomo Zambelli. Combinatorica 26 (2006) 533-558. ps version |
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. | Decomposing Berge Graphs Containing Proper Wheels, by Michele Conforti, Gerard Cornuejols, Kristina Vuskovic and Giacomo Zambelli, March 2002. ps version |
Convex Sets and Minimal Sublinear Functions, by Amitabh Basu, Gerard Cornuejols and Giacomo Zambelli. Journal of Convex Analysis 18 (2011) 427-432. 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 |
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. | Square-Free Perfect Graphs, by Michele Conforti, Gerard Cornuejols and Kristina Vuskovic. Journal of Combinatorial Theory B 90 (2004) 257-307. ps version |
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. | A Class of Berge Graphs Containing P6, by Gerard Cornuejols and Xinming Liu. Journal of Combinatorial Theory B 87 (2003) 300-330. ps version |
Equivalence between Intersection Cuts and the Corner Polyhedron, by Michele Conforti, Gerard Cornuejols and Giacomo Zambelli. Operations Research Letters 38 (2010) 153-155. | 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 |
Stable Sets, Corner Polyhedra and the Chvatal Closure, by Manoel Campelo and Gerard Cornuejols. Operations Research Letters 37 (2009) 375-378. previous version | Perfect Graphs, Partitionable Graphs and Cutsets, by Michele Conforti, Gerard Cornuejols, Grigor Gasparyan and Kristina Vuskovic. Combinatorica 22 (2002) 19-33. |
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. | 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 |
Minimal Valid Inequalities for Integer Constraints, by Valentin Borozan and Gerard Cornuejols. Mathematics of Operations Research 34 (2009) 538-546. 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 |
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 | Balanced Matrices, by Michele Conforti, Gerard Cornuejols and Kristina Vuskovic. Discrete Mathematics 306 (2006) 2411-2437. 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. | 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 |
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. | 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). |
Valid Inequalities for Mixed Integer Linear Programs, by Gerard Cornuejols. Mathematical Programming B 112 (2008) 3-44. ps version | 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 |
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 | 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 |
A Note on the MIR Closure, by Pierre Bonami and Gerard Cornuejols. Operations Research Letters 36 (2008) 4-6. | 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 |
Revival of the Gomory Cuts in the 1990's, by Gerard Cornuejols. Annals of Operations Research 149 (2007) 63-66. ps version | 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 |
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 | Ideal Clutters, by Gerard Cornuejols and Bertrand Guenin. Discrete Applied Mathematics 123 (2002) 303-338. ps version |
A Convex-Analysis Perspective on Disjunctive Cuts, by Gerard Cornuejols and Claude Lemarechal, Mathematical Programming A 106 (2006) 567-586. 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. |
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 | A Note on Dijoins, by Gerard Cornuejols and Bertrand Guenin. Discrete Mathematics 243 (2002) 213-216. |
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. | The Packing Property, by Gerard Cornuejols, Bertrand Guenin and Francois Margot. Mathematical Programming A 89 (2000) 113-126. |
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 | Recognizing Berge Graphs, by Maria Chudnovsky, Gerard Cornuejols, Xinming Liu, Paul Seymour and Kristina Vuskovic. Combinatorica 25 (2005) 143-186. 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 | 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 |
On the Rank of Mixed 0,1 Polyhedra, by Gerard Cornuejols and Yanjun Li. Mathematical Programming A 91 (2002) 391-397. | 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 311 (2007) 123-135. ps version. An earlier draft: The Strong Perfect Graph Conjecture. Proceedings of the International Congress of Mathematicians III: Invited Lectures Beijing (2002) 547-559. ps version |
Elementary Closures for Integer Programs, by Gerard Cornuejols and Yanjun Li. Operations Research Letters 28 (2001) 1-8. | Decomposing Berge Graphs Containing No Proper Wheel, Long Prism or their Complements, by Michele Conforti, Gerard Cornuejols and Giacomo Zambelli. Combinatorica 26 (2006) 533-558. ps version |