On the Matrix-Cut Rank of Polyhedra

References

  • Bockmayr A., Eisenbrand F.On the Chvátal rank of polytopes in the 0/1 cube (1997) . Research report MPI-I-97-2-009, Max-Planck-Institut für Informatik, Saarbrücken, GermanyGoogle Scholar
  • Chvátal V. Edmonds polytopes and a hierarchy of combinatorial problems. Discrete Math. (1973a) 4:305–337CrossrefGoogle Scholar
  • Chvátal V. Edmonds polytopes and weakly hamiltonian graphs. Math. Programming (1973b) 5:29–40CrossrefGoogle Scholar
  • Chvátal V., Cook W., Hartmann M. On cutting plane proofs in combinatorial optimization. Linear Algebra Appl. (1989) 114/115:455–499CrossrefGoogle Scholar
  • Dantzig G. B., Fulkerson R., Johnson S. M. Solution of a large-scale traveling salesman problem. Oper. Res. (1954) 2:393–410LinkGoogle Scholar
  • Eisenbrand F. On the membership problem for the elementary closure of a polyhedron. Combinatorica (1999) 19:297–300CrossrefGoogle Scholar
  • Eisenbrand F., Schultz A. S., Cornuéjols G., Burkard R. E., Woeginger G. J. Bounds on the Chvátal rank of polytopes in the 0/1-cube. Integer Programming and Combinatorial Optim., 7th Internat. IPCO Conf. (1999) (Springer, Berlin, Germany) 137–150CrossrefGoogle Scholar
  • Goemans M. X. Semidefinite programming in combinatorial optimization. Math. Programming (1997) 79:143–161CrossrefGoogle Scholar
  • Goemans M. X. Semidefinite programming and combinatorial optimization. Documenta Math. J. Deutschen Math (1998) III:657–666Vereinigung, Extra Volume ICMGoogle Scholar
  • Goemans M. X., Tunçel L.When does the positive semidefiniteness constraint help in lifting procedures? (2000) . Research report CORR 2000-01, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, CanadaGoogle Scholar
  • Gomory R. E. Outline of an algorithm for integer solutions to linear programs. Bull. Amer. Math. Soc. (1958) 64:275–278CrossrefGoogle Scholar
  • Grötschel M., Padberg M., Lawler E. L., Lenstra J. K., Rinnooy Kan A. H. G., Shmoys D. B. Polyhedral theory. The Traveling Salesman Problem (1985) (Wiley, Chichester, U.K.) 251–306Google Scholar
  • Jünger M., Reinelt G., Rinaldi G., Ball M., Magnanti T., Monma C. L., Nemhauser G. The traveling salesman problem. Handbook on Operations Research and Management Sciences: Networks (1995) (North-Holland, Amsterdam, The Netherlands) 225–330Google Scholar
  • Lipták L. Critical facets of the stable set polytope. (1999) . Ph.D. thesis, Yale University, Department of Mathematics, New Haven, CTGoogle Scholar
  • Lovász L., Schrijver A. Cones of matrices and set-functions and 0-1 optimization. SIAM J. Optim. (1991) 1:166–190CrossrefGoogle Scholar
  • Schrijver A., Deza M., Rosenberg I. G. On cutting planes. Combinatorics 79 Part II, Annals of Discrete Mathematics 9 (1980) (North Holland, Amsterdam, The Netherlands) 291–296CrossrefGoogle Scholar
  • Schrijver A.Theory of Linear and Integer Programming (1986) (Wiley, Chichester, U.K.) Google Scholar
  • Sherali H. D., Adams W. P. A hierarchy of relaxations between the continuous and convex representations for zero-one programming problems. SIAM J. Discrete Math. (1990) 3:411–430CrossrefGoogle Scholar
  • Stephen T., Tunçel L. On a representation of the matching polytope via semidefinite liftings. Math. Oper. Res. (1999) 24:1–7LinkGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.