Projection and lifting in combinatorial optimization

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2241, Issue , 2001, Pages 26-56

  Balas, Egon ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMBINATORIAL OPTIMIZATION; COMPUTATIONAL GEOMETRY; GEOMETRY; LINEAR PROGRAMMING; MOBILE AGENTS;

COMPACT REPRESENTATION; COMPUTATIONAL RESULTS; CONVEXIFICATION; DISJUNCTIVE CUTS; DISJUNCTIVE PROGRAMMING; EXTENDED FORMULATIONS; LIFT-AND-PROJECT; PROBLEM FORMULATION;

INTEGER PROGRAMMING;

EID: 84959062135     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45586-8_2     Document Type: Conference Paper

References (43)

1. E. Balas, “Disjunctive Programming: Properties of the Convex Hull of Feasible Points.” Invited paper, with a foreword by G. Cornuéjols and W. Pulleyblank, Discrete Applied Mathematics, 89, 1998, 3-44 (originally MSRR# 348, Carnegie Mellon University, July 1974).
2. E. Balas, “Disjunctive Programming.” Annals of Discrete Mathematics, 5, 1979, 3-51.
3. E. Balas, “Disjunctive Programming and a Hierarchy of Relaxations for Discrete Optimization Problems.” SIAM Journal on Algebraic and Discrete Methods, 6, 1985, 466-485.
4. E. Balas, “The Assignable Subgraph Polytope of a Directed Graph.” Congressus Numerantium, 60, 1987, 35-42.
5. E. Balas, “A Modified Lift-and-Project Procedure.” Mathematical Programming, 79, 1997, 19-31.
6. E. Balas, “Projection with a Minimal System of Inequalities.” Computational Optimization and Applications, 10, 1998, 189-193.
7. E. Balas, S. Ceria and G. Cornuéjols, “A Lift-and-Project Cutting Plane Algorithm for Mixed 0-1 Programs.” Mathematical Programming, 58, 1993, 295-324.
8. E. Balas, S. Ceria and G. Cornuéjols, “Mixed 0-1 Programming by Lift-and-Project in a Branch-and-Cut Framework.” Management Science, 42, 1996, 1229-1246.
9. E. Balas, S. Ceria, G. Cornuéjols and G. Pataki, “Polyhedral Methods for the Maximum Clique Problem.” In D. Johnson and M. Trick (editors), Clique, Coloring and Satisfiability: The Second DIMACS Challenge. The American Mathematical Society, Providence, RI, 1996, 11-27.
10. E. Balas and R.G. Jeroslow, “Strengthening Cuts for Mixed Integer Programs.” European Journal of Operational Research, 4, 1980, 224-234.
11. E. Balas and J.B. Mazzola, “Nonlinear 0-1 Programming: I. Linearization Techniques, II. Dominance Relations and Algorithms.” Mathematical Programming, 30, 1984, 1-21 and 22-45.
12. E. Balas and M. Oosten, “On the Dimension of Projected Polyhedra.” Discrete Applied Mathematics, 87, 1998, 1-9.
13. E. Balas and M. Oosten, “The Cycle Polytope of a Directed Graph.” Networks, 36, 2000, 34-46.
14. E. Balas and W.R. Pulleyblank, “The Perfectly Matchable Subgraph Polytope of a Bipartite Graph.” Networks, 13, 1983, 495-518.
15. E. Balas and W.R. Pulleyblank, “The Perfectly Matchable Subgraph Polytope of an Arbitrary Graph.” Combinatorica, 9, 1989, 321-337.
16. E. Balas, J. Tama and J. Tind, “Sequential Convexification in Reverse Convex and Disjunctive Programming.” Mathematical Programming, 44, 1989, 337-350.
17. N. Beaumont, “An Algorithm for Disjunctive Programming.” European Journal of Operational Research, 48, 1990, 362-371.
18. R. Bixby, W. Cook, A. Cox and E. Lee, “Computational Experience with Parallel Mixed Integer Programming in a Distributed Environment.” Annals of Operations Research, 90, 1999, 19-45.
19. C. Blair, “Two Rules for Deducing Valid Inequalities for 0-1 Programs.” SIAM Journal of Applied Mathematics, 31, 1976, 614-617.
20. C. Blair, “Facial Disjunctive Programs and Sequences of Cutting Planes.” Discrete Applied Mathematics, 2, 1980, 173-180.
21. S. Ceria and G. Pataki, “Solving Integer and Disjunctive Programs by Lift-and-Project.” In R.E. Bixby, E.A. Boyd and R.Z. Rios-Mercado (editors), IPCO VI, Lecture Notes in Computer Science, 1412, Springer 1998, 271-283.
22. S. Ceria and J. Soares, “Disjunctive Cuts for Mixed 0-1 Programming: Duality and Lifting.” GSB, Columbia University, 1997.
23. S. Ceria and J. Soares, “Convex Programming for Disjunctive Convex Optimization.” Mathematical Programming, 86, 1999, 595-614.
24. G.B. Dantzig, R.D. Fulkerson and S.M. Johnson, “Solution of a Large-Scale Traveling Salesman Problem.” Operations Research, 2, 1954, 393-410.
25. R. Fortet, “Applications de l’algèbre de Boolean recherche opérationnelle.” Revue Francaise de Recherche Opérationnelle, 4, 1960, 17-25.
26. R.G. Jeroslow, “Cutting Plane Theory: Disjunctive Methods.” Annals of Discrete Mathematics, 1, 1977, 293-330.
27. R.G. Jeroslow, “Representability in Mixed Integer Programming I: Characterization Results.” Discrete Applied Mathematics, 17, 1987, 223-243.
28. R.G. Jeroslow, “Logic Based Decision Support: Mixed Integer Model Formulation.” Annals of Discrete Mathematics, 40, 1989.
29. E.L. Johnson, “The Group Problem for Mixed-Integer Programming.” Mathematical Programming Study, 2, 1974, 137-179.
30. A. Letchford, “On Disjunctive Cuts for Combinatorial Optimization.” Journal of Combinatorial Optimization, 5, 2001 (Issue 3).
31. L. Lovász and A. Schrijver, “Cones of Matrices and Set Functions and 0-1 Optimization.” SIAM Journal of Optimization, 1, 1991, 166-190.
32. C.E. Miller, A.W. Tucker and R.A. Zemlin, “Integer Programming Formulations and Traveling Salesman Problems.” Journal of the ACM, 7, 1960, 326-329.
33. G. Nemhauser and L. Wolsey, Integer and Combinatorial Optimization, Wiley, 1986.
34. M. Padberg and Ting-Yi Sung, “An Analytical Comparison of Different Formulations of the Traveling Salesman Problem.” Math. Programming, 52, 1991, 315-357.
35. G. Pataki, personal communication, March 2001.
36. M. Perregaard and E. Balas, “Generating Cuts from Multiple-Term Disjunctions.” In K. Aardal and B. Gerards (Editors), Integer Programming and Combinatorial Optimization (8th IPCO Conference, Utrecht, 2001), LCNS No. 2081, Springer, 2001.
37. H. Sherali and W. Adams, “A Hierarchy of Relaxations Between the Continuous and Convex Hull Representations for Zero-One Programming Problems.” SIAM Journal on Discrete Mathematics, 3, 1990, 411-430.
38. H. Sherali and C. Shetty, Optimization with Disjunctive Constraints. Lecture Notes in Economics and Mathematical Systems, 181, Springer, 1980.
39. J. Stoer and C. Witzgall, Convexity and Optimization in Finite Dimensions I. Springer, 1970.
40. R.A. Stubbs and S. Mehrotra, “A Branch-and-Cut Method for 0-1 Mixed Convex Programming.” Department of Industrial Engineering, Northwestern University, 1996.
41. S. Thienel, “ABACUS: A Branch-and-Cut System.” Doctoral Dissertation, Faculty of Mathematics and The Natural Sciences, University of Cologne, 1995.
42. M. Turkay and I.E. Grossmann, “Disjunctive Programming Techniques for the Optimization of Process Systems with Discontinuous Investment Costs-Multiple Size Regions.” Industrial Engineering Chemical Research, 35, 1996, 2611-2623.
43. H.P. Williams, “An Alternative Explanation of Disjunctive Formulations.” European Journal of Operational Research, 72, 1994, 200-203.