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Volumn 18, Issue 1, 2007, Pages 87-105

Computing the stability number of a graph via linear and semidefinite programming

Author keywords

Copositivity; Lifting procedures; Polynomials; Stability number

Indexed keywords

COPOSITIVITY; LIFTING PROCEDURES; SEMIDEFINITE PROGRAMMING; STABILITY NUMBER;

EID: 39449110450     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/05064401X     Document Type: Article
Times cited : (87)

References (17)
  • 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. Program., 58 (1993), pp. 295-324.
    • (1993) Math. Program , vol.58 , pp. 295-324
    • BALAS, E.1    CERIA, S.2    CORNUÉJOLS, G.3
  • 2
    • 39449097845 scopus 로고    scopus 로고
    • I. BOMZE, M. BUDINICH, P. PARDALOS, AND M. PELILLO, The Maximum Clique Problem, in Handb. Combin. Opt., Suppl. A, D. Du and P. Pardalos, eds., Kluwer Academic Publishers, Norwell, MA, 1999.
    • I. BOMZE, M. BUDINICH, P. PARDALOS, AND M. PELILLO, The Maximum Clique Problem, in Handb. Combin. Opt., Suppl. A, D. Du and P. Pardalos, eds., Kluwer Academic Publishers, Norwell, MA, 1999.
  • 3
    • 31244435061 scopus 로고    scopus 로고
    • Solving standard quadratic optimization problems via semidefinite and copositive programming
    • I. BOMZE AND E. DE KLERK, Solving standard quadratic optimization problems via semidefinite and copositive programming, J. Global Optim., 24 (2002), pp. 163-185.
    • (2002) J. Global Optim , vol.24 , pp. 163-185
    • BOMZE, I.1    DE KLERK, E.2
  • 4
    • 0036433723 scopus 로고    scopus 로고
    • Approximation of the stability number of a graph via copositive programming
    • E. DE KLERK AND D. PASECHNIK, Approximation of the stability number of a graph via copositive programming, SIAM J. Optim., 12 (2002), pp. 875-892.
    • (2002) SIAM J. Optim , vol.12 , pp. 875-892
    • DE KLERK, E.1    PASECHNIK, D.2
  • 5
    • 0002106815 scopus 로고
    • On non-negative forms in real variables some or all of which are non-negative
    • P. DIANANDA, On non-negative forms in real variables some or all of which are non-negative, Math. Proc. Cambridge Philos. Soc., 58 (1962), pp. 17-25.
    • (1962) Math. Proc. Cambridge Philos. Soc , vol.58 , pp. 17-25
    • DIANANDA, P.1
  • 6
    • 24944588682 scopus 로고    scopus 로고
    • Semidefinite bounds for the stability number of a graph via sums of squares of polynomials
    • Lecture Notes in Comput. Sci. 3509/2005, Springer, Berlin
    • N. GVOZDENOVIĆ AND M. LAURENT, Semidefinite bounds for the stability number of a graph via sums of squares of polynomials, in Integer Programming and Combinatorial Optimization, Lecture Notes in Comput. Sci. 3509/2005, Springer, Berlin, 2005, pp. 136-151.
    • (2005) Integer Programming and Combinatorial Optimization , pp. 136-151
    • GVOZDENOVIĆ, N.1    LAURENT, M.2
  • 7
    • 0000109157 scopus 로고    scopus 로고
    • 1-ε|, Acta Math., 182 (1999), pp. 105-142.
    • 1-ε|, Acta Math., 182 (1999), pp. 105-142.
  • 9
    • 0035238864 scopus 로고    scopus 로고
    • Global optimization problems with polynomials and the problem of moments
    • J. LASSERRE, Global optimization problems with polynomials and the problem of moments, SIAM J. Optim., 11 (2001), pp. 796-817.
    • (2001) SIAM J. Optim , vol.11 , pp. 796-817
    • LASSERRE, J.1
  • 10
    • 0036351765 scopus 로고    scopus 로고
    • An explicit equivalent positive semidefinite program for nonlinear 0-1 programs
    • J. LASSERRE, An explicit equivalent positive semidefinite program for nonlinear 0-1 programs, SIAM J. Optim., 12 (2002), pp. 756-769.
    • (2002) SIAM J. Optim , vol.12 , pp. 756-769
    • LASSERRE, J.1
  • 11
    • 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
  • 12
    • 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
  • 13
    • 0023452095 scopus 로고
    • Some NP-complete problems in quadratic and linear programming
    • K. MURTY AND S. KABADI, Some NP-complete problems in quadratic and linear programming, Math. Program., 39 (1987), pp. 117-129.
    • (1987) Math. Program , vol.39 , pp. 117-129
    • MURTY, K.1    KABADI, S.2
  • 14
    • 39449115992 scopus 로고    scopus 로고
    • Structured Semidefinite Programming and Algebraic Geometry Methods in Robustness and Optimization, Ph.D. thesis, California Institute of Technology, Pasadena, CA
    • P. PARRILO, Structured Semidefinite Programming and Algebraic Geometry Methods in Robustness and Optimization, Ph.D. thesis, California Institute of Technology, Pasadena, CA, 2000.
    • (2000)
    • PARRILO, P.1
  • 15
    • 0018492534 scopus 로고
    • A comparison of Delsarte and Lovász bounds
    • A. SCHRIJVER, A comparison of 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
  • 16
    • 0033296299 scopus 로고    scopus 로고
    • Using SeDuMi 1.02, a Matlab toolbox for optimization over symmetric cones
    • J. STURM, Using SeDuMi 1.02, a Matlab toolbox for optimization over symmetric cones, Optim. Methods Softw., 11-12 (1999), pp. 545-581.
    • (1999) Optim. Methods Softw , vol.11-12 , pp. 545-581
    • STURM, J.1
  • 17
    • 33750900187 scopus 로고    scopus 로고
    • LMI approximations for cones of positive semidefinite forms
    • L. ZULUAGA, J. VERA, AND J. PEÑA, LMI approximations for cones of positive semidefinite forms, SIAM J. Optim., 16 (2006), 1076-1091.
    • (2006) SIAM J. Optim , vol.16 , pp. 1076-1091
    • ZULUAGA, L.1    VERA, J.2    PEÑA, J.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.