메뉴 건너뛰기




Volumn 156, Issue 1, 2008, Pages 25-41

Unification of lower-bound analyses of the lift-and-project rank of combinatorial optimization polyhedra

Author keywords

Integer programming; Lift and project; Semidefinite lifting; Semidefinite programming

Indexed keywords

COMPUTATIONAL METHODS; INTEGER PROGRAMMING; ITERATIVE METHODS; PROBLEM SOLVING;

EID: 35649006008     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2007.07.021     Document Type: Article
Times cited : (8)

References (31)
  • 1
    • 0242271908 scopus 로고    scopus 로고
    • Lift and project relaxations for the matching and related polytopes
    • Aguilera N.E., Bianchi S.M., and Nasini G.L. Lift and project relaxations for the matching and related polytopes. Discrete Appl. Math. 134 (2004) 193-212
    • (2004) Discrete Appl. Math. , vol.134 , pp. 193-212
    • Aguilera, N.E.1    Bianchi, S.M.2    Nasini, G.L.3
  • 2
    • 0036953711 scopus 로고    scopus 로고
    • S. Arora, B. Bollobás, L. Lovász, Proving integrality gaps without knowing the linear program, Proceedings of the 43rd IEEE Symposium FOCS, 2002, pp. 313-322.
  • 3
    • 35648990002 scopus 로고    scopus 로고
    • E. Balas, Disjunctive programming: properties of the convex hull of feasible points. Management Science Research Report 348 GSIA, Carnegie Mellon University, Pittsburgh, PA, USA, 1974 (Appeared as: E. Balas. Disjunctive programming: properties of the convex hull of feasible points. Discrete Appl. Math. 89 (1998) 3-44.)
  • 4
    • 0000185277 scopus 로고
    • A lift-and-project cutting plane algorithm for mixed 0-1 programs
    • Balas E., Ceria S., and Cornuéjols G. A lift-and-project cutting plane algorithm for mixed 0-1 programs. Math. Programming A 58 (1993) 295-323
    • (1993) Math. Programming A , vol.58 , pp. 295-323
    • Balas, E.1    Ceria, S.2    Cornuéjols, G.3
  • 5
    • 13944252972 scopus 로고    scopus 로고
    • Tree-width and the Sherali-Adams operator
    • Bienstock D., and Ozbay N. Tree-width and the Sherali-Adams operator. Discrete Optim. 1 (2004) 13-21
    • (2004) Discrete Optim. , vol.1 , pp. 13-21
    • Bienstock, D.1    Ozbay, N.2
  • 6
    • 14944344548 scopus 로고    scopus 로고
    • Subset algebra lift operators for 0-1 integer programming
    • Bienstock D., and Zuckerberg M. Subset algebra lift operators for 0-1 integer programming. SIAM J. Optim. 15 (2004) 63-95
    • (2004) SIAM J. Optim. , vol.15 , pp. 63-95
    • Bienstock, D.1    Zuckerberg, M.2
  • 7
    • 0000971541 scopus 로고
    • Edmonds polytopes and a hierarchy of combinatorial problems
    • Chvátal V. Edmonds polytopes and a hierarchy of combinatorial problems. Discrete Math. 4 (1973) 33-41
    • (1973) Discrete Math. , vol.4 , pp. 33-41
    • Chvátal, V.1
  • 8
    • 0007679136 scopus 로고
    • On cutting plane proofs in combinatorial optimization
    • Chvátal V., Cook W., and Hartmann M. On cutting plane proofs in combinatorial optimization. Linear Algebra Appl. 114/115 (1989) 455-499
    • (1989) Linear Algebra Appl. , vol.114-115 , pp. 455-499
    • Chvátal, V.1    Cook, W.2    Hartmann, M.3
  • 9
    • 33646719965 scopus 로고    scopus 로고
    • On Lovász-Schrijver lift-and-project procedures on the Dantzig-Fulkerson-Johnson relaxation of the TSP
    • Cheung K.K.H. On Lovász-Schrijver lift-and-project procedures on the Dantzig-Fulkerson-Johnson relaxation of the TSP. SIAM J. Optim. 16 (2005) 380-399
    • (2005) SIAM J. Optim. , vol.16 , pp. 380-399
    • Cheung, K.K.H.1
  • 10
    • 0035261799 scopus 로고    scopus 로고
    • On the matrix-cut rank of polyhedra
    • Cook W., and Dash S. On the matrix-cut rank of polyhedra. Math. Oper. Res. 26 (2001) 19-30
    • (2001) Math. Oper. Res. , vol.26 , pp. 19-30
    • Cook, W.1    Dash, S.2
  • 11
    • 0348117745 scopus 로고
    • An interrelation between line graphs, eigenvalues and matroids
    • Doob M. An interrelation between line graphs, eigenvalues and matroids. J. Combin. Theory B 15 (1973) 40-50
    • (1973) J. Combin. Theory B , vol.15 , pp. 40-50
    • Doob, M.1
  • 12
    • 0141543721 scopus 로고    scopus 로고
    • Bounds on the Chvátal rank of polytopes in the 0/1 cube
    • Eisenbrand F., and Schulz A.S. Bounds on the Chvátal rank of polytopes in the 0/1 cube. Combinatorica 23 (2003) 245-261
    • (2003) Combinatorica , vol.23 , pp. 245-261
    • Eisenbrand, F.1    Schulz, A.S.2
  • 13
    • 0038285474 scopus 로고    scopus 로고
    • The probable value of the Lovasz-Schrijver relaxations for maximum independent set
    • Feige U., and Krauthgamer R. The probable value of the Lovasz-Schrijver relaxations for maximum independent set. SIAM J. Comput. 32 (2003) 345-370
    • (2003) SIAM J. Comput. , vol.32 , pp. 345-370
    • Feige, U.1    Krauthgamer, R.2
  • 14
    • 2942659750 scopus 로고    scopus 로고
    • Symmetry groups, semidefinite programs, and sums of squares
    • Gatermann K., and Parrilo P.A. Symmetry groups, semidefinite programs, and sums of squares. J. Pure Appl. Algebra 192 (2004) 95-128
    • (2004) J. Pure Appl. Algebra , vol.192 , pp. 95-128
    • Gatermann, K.1    Parrilo, P.A.2
  • 15
    • 0347504564 scopus 로고    scopus 로고
    • Semidefinite programs and association schemes
    • Goemans M.X., and Rendl F. Semidefinite programs and association schemes. Computing 63 (1999) 331-340
    • (1999) Computing , vol.63 , pp. 331-340
    • Goemans, M.X.1    Rendl, F.2
  • 16
    • 0035518191 scopus 로고    scopus 로고
    • When does the positive semidefiniteness constraint help in lifting procedures?
    • Goemans M.X., and Tunçel L. When does the positive semidefiniteness constraint help in lifting procedures?. Math. Oper. Res. 26 (2001) 796-815
    • (2001) Math. Oper. Res. , vol.26 , pp. 796-815
    • Goemans, M.X.1    Tunçel, L.2
  • 17
    • 35648964197 scopus 로고    scopus 로고
    • D. Grigoriev, E.A. Hirsch, D.V. Pasechnik, Complexity of semi-algebraic proofs, Electronic Colloquium on Computational Complexity, revision 3 of report no. 103, 2001.
  • 18
    • 0040214558 scopus 로고    scopus 로고
    • Cones of matrices and successive convex relaxations of nonconvex sets
    • Kojima M., and Tunçel L. Cones of matrices and successive convex relaxations of nonconvex sets. SIAM J. Optim. 10 (2000) 750-778
    • (2000) SIAM J. Optim. , vol.10 , pp. 750-778
    • Kojima, M.1    Tunçel, L.2
  • 19
    • 39649093787 scopus 로고    scopus 로고
    • An explicit exact SDP relaxation for nonlinear 0-1 programs
    • Aardal K., and Gerards A.M.H. (Eds)
    • Lasserre J.B. An explicit exact SDP relaxation for nonlinear 0-1 programs. In: Aardal K., and Gerards A.M.H. (Eds). Lecture Notes in Computer Science (2001) 293-303
    • (2001) Lecture Notes in Computer Science , pp. 293-303
    • Lasserre, J.B.1
  • 20
    • 0036034519 scopus 로고    scopus 로고
    • Polynomials nonnegative on a grid and discrete optimization
    • Lasserre J.B. Polynomials nonnegative on a grid and discrete optimization. Trans. Amer. Math. Soc. 354 (2002) 631-649
    • (2002) Trans. Amer. Math. Soc. , vol.354 , pp. 631-649
    • Lasserre, J.B.1
  • 21
    • 0036013026 scopus 로고    scopus 로고
    • Tighter linear and semidefinite relaxations for max-cut based on the Lovász-Schrijver lift-and-project procedure
    • Laurent M. Tighter linear and semidefinite relaxations for max-cut based on the Lovász-Schrijver lift-and-project procedure. SIAM J. Optim. 12 (2002) 345-375
    • (2002) SIAM J. Optim. , vol.12 , pp. 345-375
    • Laurent, M.1
  • 22
    • 3142703556 scopus 로고    scopus 로고
    • Lower bound for the number of iterations in semidefinite hierarchies for the cut polytope
    • Laurent M. Lower bound for the number of iterations in semidefinite hierarchies for the cut polytope. Math. Oper. Res. 28 (2003) 871-883
    • (2003) Math. Oper. Res. , vol.28 , pp. 871-883
    • Laurent, M.1
  • 23
    • 35648945285 scopus 로고    scopus 로고
    • L. Lipták, Critical facets of the stable set polytope, Ph.D. Thesis, Yale University, 1999.
  • 24
    • 79959971337 scopus 로고    scopus 로고
    • The stable set problem and the lift-and-project ranks of graphs
    • Lipták L., and Tunçel L. The stable set problem and the lift-and-project ranks of graphs. Math. Programming 98 (2003) 319-353
    • (2003) Math. Programming , vol.98 , pp. 319-353
    • Lipták, L.1    Tunçel, L.2
  • 26
    • 0001154274 scopus 로고
    • Cones of matrices and set-functions and 0-1 optimization
    • Lovász L., and Schrijver A. Cones of matrices and set-functions and 0-1 optimization. SIAM J. Optim. 1 (1991) 166-190
    • (1991) SIAM J. Optim. , vol.1 , pp. 166-190
    • Lovász, L.1    Schrijver, A.2
  • 27
    • 0001321687 scopus 로고
    • A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems
    • Sherali H.D., and Adams W.P. A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems. SIAM J. Discrete Math. 3 (1990) 411-430
    • (1990) SIAM J. Discrete Math. , vol.3 , pp. 411-430
    • Sherali, H.D.1    Adams, W.P.2
  • 28
    • 0003493079 scopus 로고    scopus 로고
    • A reformulation-linearization technique for solving discrete and continuous nonconvex problems
    • Sherali H.D., and Adams W.P. A reformulation-linearization technique for solving discrete and continuous nonconvex problems. Nonconvex Optim. Appl. 31 (1999)
    • (1999) Nonconvex Optim. Appl. , vol.31
    • Sherali, H.D.1    Adams, W.P.2
  • 29
    • 0006222852 scopus 로고    scopus 로고
    • Tighter representations for set partitioning problems
    • Sherali H.D., and Lee Y. Tighter representations for set partitioning problems. Discrete Appl. Math. 68 (1996) 153-167
    • (1996) Discrete Appl. Math. , vol.68 , pp. 153-167
    • Sherali, H.D.1    Lee, Y.2
  • 30
    • 0344642581 scopus 로고    scopus 로고
    • On a representation of the matching polytope via semidefinite liftings
    • Stephen T., and Tunçel L. On a representation of the matching polytope via semidefinite liftings. Math. Oper. Res. 24 (1999) 1-7
    • (1999) Math. Oper. Res. , vol.24 , pp. 1-7
    • Stephen, T.1    Tunçel, L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.