메뉴 건너뛰기




Volumn 13, Issue 4, 2003, Pages 1014-1028

Computational experience with stable set relaxations

Author keywords

Semidefinite programming; Stable set problem; Theta function

Indexed keywords


EID: 0242511176     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623401394092     Document Type: Article
Times cited : (39)

References (27)
  • 1
    • 0000185277 scopus 로고
    • A lift-and-project cutting plane algorithm for mixed 0-1 programs
    • E. BALAS, S. CERIA, AND G. CORNUÉJOLS, A lift-and-project cutting plane algorithm for mixed 0-1 programs, Math. Programming, 58 (1993), pp. 295-324.
    • (1993) Math. Programming , vol.58 , pp. 295-324
    • Balas, E.1    Ceria, S.2    Cornuéjols, G.3
  • 2
    • 0027610254 scopus 로고
    • On cuts and matchings in planar graphs
    • F. BARAHONA, On cuts and matchings in planar graphs, Math. Programming, 36 (1993), pp. 53-68.
    • (1993) Math. Programming , vol.36 , pp. 53-68
    • Barahona, F.1
  • 3
    • 0002450116 scopus 로고    scopus 로고
    • Evolutionary approach to the maximum clique problem: Empirical evidence on a larger scale
    • I. M. Bomze, T. Csendes, R. Horst, and P. M. Pardalos, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands
    • I. M. BOMZE, M. PELILLO, AND R. GIACOMINI, Evolutionary approach to the maximum clique problem: Empirical evidence on a larger scale, in Developments in Global Optimization, I. M. Bomze, T. Csendes, R. Horst, and P. M. Pardalos, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, 1997, pp. 95-108.
    • (1997) Developments in Global Optimization , pp. 95-108
    • Bomze, I.M.1    Pelillo, M.2    Giacomini, R.3
  • 4
    • 0002716241 scopus 로고
    • On certain polytopes associated with graphs
    • V. CHVÁTAL, On certain polytopes associated with graphs, J. Combin. Theory Ser. B, 18 (1975), pp. 138-154.
    • (1975) J. Combin. Theory Ser. B , vol.18 , pp. 138-154
    • Chvátal, V.1
  • 5
    • 0242671662 scopus 로고
    • On the perfect graph theorem
    • T. C. Hu and S. M. Robinson, eds., Academic Press, New York
    • D. R. FULKERSON, On the perfect graph theorem, in Mathematical Programming, T. C. Hu and S. M. Robinson, eds., Academic Press, New York, 1973, pp. 69-76.
    • (1973) Mathematical Programming , pp. 69-76
    • Fulkerson, D.R.1
  • 6
    • 51249185617 scopus 로고
    • The ellipsoid method and its consequences in combinatorial optimization
    • M. GRÖTSCHEL, L. LOVÁSZ, AND A. SCHRIJVER, The ellipsoid method and its consequences in combinatorial optimization, Combinatorica, 1 (1981), pp. 169-197.
    • (1981) Combinatorica , vol.1 , pp. 169-197
    • Grötschel, M.1    Lovász, L.2    Schrijver, A.3
  • 9
    • 0008523984 scopus 로고    scopus 로고
    • Ph.D. thesis, University of Technology, Graz, Austria, Shaker Verlag, Aachen, Germany, Maastricht, The Netherlands
    • G. GRUBER, On Semidefinite Programming and Applications in Combinatorial Optimization, Ph.D. thesis, University of Technology, Graz, Austria, Shaker Verlag, Aachen, Germany, Maastricht, The Netherlands, 2000.
    • (2000) On Semidefinite Programming and Applications in Combinatorial Optimization
    • Gruber, G.1
  • 10
    • 0007154687 scopus 로고
    • Test case generators and computational results for the maximum clique problem
    • J. HASSELBERG, P. M. PARDALOS, AND G. VAIRAKTARAKIS, Test case generators and computational results for the maximum clique problem, J. Global Optim., 3 (1993), pp. 463-482.
    • (1993) J. Global Optim. , vol.3 , pp. 463-482
    • Hasselberg, J.1    Pardalos, P.M.2    Vairaktarakis, G.3
  • 11
    • 84948976359 scopus 로고
    • Combining semidefinite and polyhedral relaxations for integer programs
    • Integer Programming and Combinatorial Optimization (Proceedings of the 4th International IPCO Conference, Copenhagen, Denmark), E. Balas and J. Clausen, eds., Springer-Verlag, Berlin, 1995
    • C. HELMBERG, S. POLJAK, F. RENDL, AND H. WOLKOWICZ, Combining semidefinite and polyhedral relaxations for integer programs, in Integer Programming and Combinatorial Optimization (Proceedings of the 4th International IPCO Conference, Copenhagen, Denmark, 1995), Lecture Notes in Comput. Sci. 920, E. Balas and J. Clausen, eds., Springer-Verlag, Berlin, 1995, pp. 124-134.
    • (1995) Lecture Notes in Comput. Sci. , vol.920 , pp. 124-134
    • Helmberg, C.1    Poljak, S.2    Rendl, F.3    Wolkowicz, H.4
  • 13
    • 0031542833 scopus 로고    scopus 로고
    • Interior-point methods for the monotone semidefinite linear complementarity problem in symmetric matrices
    • M. KOJIMA, S. SHINDOH, AND S. HARA, Interior-point methods for the monotone semidefinite linear complementarity problem in symmetric matrices, SIAM J. Optim., 7 (1997), pp. 86125.
    • (1997) SIAM J. Optim. , vol.7 , pp. 86125
    • Kojima, M.1    Shindoh, S.2    Hara, S.3
  • 14
    • 0003458234 scopus 로고    scopus 로고
    • A Comparison of the Sherali-Adams, Lovász-Schrijver and Lasserre Relaxations for 0-1 Programming
    • Centrum voor Wiskunde en Informatica (CWI), Amsterdam
    • M. LAURENT, A Comparison of the Sherali-Adams, Lovász-Schrijver and Lasserre Relaxations for 0-1 Programming, Technical report, Centrum voor Wiskunde en Informatica (CWI), Amsterdam, 2001.
    • (2001) Technical Report
    • Laurent, M.1
  • 15
    • 0031144411 scopus 로고    scopus 로고
    • Connections between semidefinite relaxations of the max-cut and stable set problems
    • M. LAURENT, S. POLJAK, AND F. RENDL, Connections between semidefinite relaxations of the max-cut and stable set problems, Math. Programming, 77 (1997), pp. 225-246.
    • (1997) Math. Programming , vol.77 , pp. 225-246
    • Laurent, M.1    Poljak, S.2    Rendl, F.3
  • 16
    • 0006355286 scopus 로고    scopus 로고
    • Semidefinite Relaxations and Lagrangian Duality with Application to Combinatorial Optimization
    • Institut National de Recherche en Informatique et en Automatique (INRIA), St. Martin, France
    • C. LEMARÉCHAL AND F. OUSTRY, Semidefinite Relaxations and Lagrangian Duality with Application to Combinatorial Optimization, Technical report, Institut National de Recherche en Informatique et en Automatique (INRIA), St. Martin, France, 1999.
    • (1999) Technical Report
    • Lemaréchal, C.1    Oustry, F.2
  • 17
    • 0018292109 scopus 로고
    • On the Shannon capacity of a graph
    • L. LOVÁSZ, On the Shannon capacity of a graph, IEEE Trans. Inform. Theory, 25 (1979), pp. 1-7.
    • (1979) IEEE Trans. Inform. Theory , vol.25 , pp. 1-7
    • Lovász, L.1
  • 18
    • 30744463727 scopus 로고
    • Semidefinite Programs and Combinatorial Optimization
    • L. LOVÁSZ, Semidefinite Programs and Combinatorial Optimization, lecture notes, 1995.
    • (1995) Lecture Notes
    • Lovász, L.1
  • 19
    • 0001154274 scopus 로고
    • Cones of matrices and set-functions and 0-1 optimization
    • L. LOVÁSZ AND A. SCHRIJVER, Cones of matrices and set-functions and 0-1 optimization, SIAM J. Optim., 1 (1991), pp. 166-190.
    • (1991) SIAM J. Optim. , vol.1 , pp. 166-190
    • Lovász, L.1    Schrijver, A.2
  • 21
    • 0031285899 scopus 로고    scopus 로고
    • Primal-dual path-following algorithms for semidefinite programming
    • R. D. C. MONTEIRO, Primal-dual path-following algorithms for semidefinite programming, SIAM J. Optim., 7 (1997), pp. 663-678.
    • (1997) SIAM J. Optim. , vol.7 , pp. 663-678
    • Monteiro, R.D.C.1
  • 22
    • 0003254248 scopus 로고
    • Interior-point Polynomial Algorithms in Convex Programming
    • Siam, Philadelphia
    • Y. NESTEROV AND A. NEMIROVSKII, Interior-Point Polynomial Algorithms in Convex Programming, SIAM Stud. Appl. Math. 13, SIAM, Philadelphia, 1994.
    • (1994) Siam Stud. Appl. Math. , vol.13
    • Nesterov, Y.1    Nemirovskii, A.2
  • 23
    • 0002821681 scopus 로고
    • A recipe for semidefinite relaxation for (0, 1)-quadratic programming
    • S. POLJAK, F. RENDL, AND H. WOLKOWICZ, A recipe for semidefinite relaxation for (0, 1)-quadratic programming, J. Global Optim., 7 (1995), pp. 51-73.
    • (1995) J. Global Optim. , vol.7 , pp. 51-73
    • Poljak, S.1    Rendl, F.2    Wolkowicz, H.3
  • 25
    • 0018492534 scopus 로고
    • A comparison of the Delsarte and Lovász bounds
    • A. SCHRIJVER, A comparison of the Delsarte and Lovász bounds, IEEE Trans. Inform. Theory, 25 (1979), pp. 425-429.
    • (1979) IEEE Trans. Inform. Theory , vol.25 , pp. 425-429
    • Schrijver, A.1
  • 26
    • 0001321687 scopus 로고
    • A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems
    • H. D. SHERALI AND W. P. ADAMS, A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems, SIAM J. Discrete Math., 3 (1990), pp. 411-430.
    • (1990) SIAM J. Discrete Math. , vol.3 , pp. 411-430
    • Sherali, H.D.1    Adams, W.P.2
  • 27
    • 0002085026 scopus 로고
    • The cut polytope and the Boolean quadric polytope
    • C. DE SIMONE, The cut polytope and the Boolean quadric polytope, Discrete Math., 79 (1989), pp. 71-75.
    • (1989) Discrete Math. , vol.79 , pp. 71-75
    • De Simone, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.