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Volumn 10, Issue 2, 1999, Pages 443-461

Solving large-scale sparse semidefinite programs for combinatorial optimization

Author keywords

Dual potential reduction algorithm; Maximum cut problem; Semidefinite programming

Indexed keywords


EID: 0039772219     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/s1052623497328008     Document Type: Article
Times cited : (214)

References (37)
  • 1
    • 0000110392 scopus 로고
    • An implementation of karmarkar's algorithm for linear programming
    • errata, Math. Programming, 50 (1991), p. 415
    • I. ADLER, N. K. KARMARKAR, M. G. C. RESENDE, AND G. VEIGA, An implementation of Karmarkar's algorithm for linear programming, Math. Programming, 44 (1989), pp. 297-335; errata, Math. Programming, 50 (1991), p. 415.
    • (1989) Math. Programming , vol.44 , pp. 297-335
    • Adler, I.1    Karmarkar, N.K.2    Resende, M.G.C.3    Veiga, G.4
  • 6
    • 0013378811 scopus 로고    scopus 로고
    • Sparse numerical linear algebra: Direct methods and preconditioning
    • Clarendon Press, Oxford, UK
    • I. S. DUFF, Sparse numerical linear algebra: Direct methods and preconditioning, in The State of the Art in Numerical Analysis, Clarendon Press, Oxford, UK, 1997 pp. 27-62.
    • (1997) The State of the Art in Numerical Analysis , pp. 27-62
    • Duff, I.S.1
  • 7
    • 3342875237 scopus 로고
    • A computational study of graph partitioning
    • J. FALKNER, F. RENDL, AND H. WOLKOWICZ, A computational study of graph partitioning, Math. Programming, 66 (1994), pp. 211-240.
    • (1994) Math. Programming , vol.66 , pp. 211-240
    • Falkner, J.1    Rendl, F.2    Wolkowicz, H.3
  • 9
    • 0000201892 scopus 로고    scopus 로고
    • Semidefinite programming relaxation for nonconvex quadratic programs
    • T. FUJIE AND M. KOJIMA, Semidefinite programming relaxation for nonconvex quadratic programs, J. Global Optim., 10 (1997), pp. 367-380.
    • (1997) J. Global Optim. , vol.10 , pp. 367-380
    • Fujie, T.1    Kojima, M.2
  • 11
    • 84893574327 scopus 로고
    • Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
    • M. X. GOEMANS AND D. P. WILLIAMSON, Improved approximation algorithms for Maximum Cut and Satisfiability problems using semidefinite programming, J. Assoc. Comput. Mach., 42 (1995), pp. 1115-1145.
    • (1995) J. Assoc. Comput. Mach. , vol.42 , pp. 1115-1145
    • Goemans, M.X.1    Williamson, D.P.2
  • 12
    • 0041140583 scopus 로고    scopus 로고
    • ZIB Preprint SC 97-37, Konrad-Zuse-Zentrum für Informationstechnik Berlin, Takustrasse 7, D-14195 Berlin, Germany
    • C. HELMBERG AND F. RENDL, A Spectral Bundle Method for Semidefinite Programming, ZIB Preprint SC 97-37, Konrad-Zuse-Zentrum für Informationstechnik Berlin, Takustrasse 7, D-14195 Berlin, Germany, 1997.
    • (1997) A Spectral Bundle Method for Semidefinite Programming
    • Helmberg, C.1    Rendl, F.2
  • 15
    • 51249181779 scopus 로고
    • A new polynomial-time algorithm for linear programming
    • N. KARMARKAR, A new polynomial-time algorithm for linear programming, Combinatorica 4 (1984), pp. 373-395.
    • (1984) Combinatorica , vol.4 , pp. 373-395
    • Karmarkar, N.1
  • 16
    • 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. 86-125.
    • (1997) SIAM J. Optim. , vol.7 , pp. 86-125
    • Kojima, M.1    Shindoh, S.2    Hara, S.3
  • 18
    • 0018292109 scopus 로고
    • On the shannon capacity of a graph
    • L. LOVÁSZ, On the Shannon capacity of a graph, IEEE Trans. Inform. Theory, IT-25 (1979), pp. 1-7.
    • (1979) IEEE Trans. Inform. Theory , vol.IT-25 , pp. 1-7
    • Lovász, L.1
  • 19
    • 0001154274 scopus 로고
    • Cones of matrices and set-functions and 0-1 optimization
    • L. LOVÁSZ AND A. SHRIJVER, 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    Shrijver, A.2
  • 21
    • 0001343365 scopus 로고    scopus 로고
    • A unified analysis for a class of path-following primal-dual interior-point algorithms for semidefinite programming
    • R. D. C. MONTEIRO AND Y. ZHANG, A Unified Analysis for a Class of Path-Following Primal-Dual Interior-Point Algorithms for Semidefinite Programming, Math. Programming, 81 (1998), pp. 281-299.
    • (1998) Math. Programming , vol.81 , pp. 281-299
    • Monteiro, R.D.C.1    Zhang, Y.2
  • 25
    • 0003254248 scopus 로고
    • Interior-point polynomial methods in convex programming
    • SIAM, Philadelphia, PA
    • YU. E. NESTEROV AND A. NEMIROVSKII, Interior-Point Polynomial Methods in Convex Programming, SIAM Stud. Appl. Math. 13, SIAM, Philadelphia, PA, 1994.
    • (1994) SIAM Stud. Appl. Math. , vol.13
    • Nesterov, Y.U.E.1    Nemirovskii, A.2
  • 26
    • 0032222088 scopus 로고    scopus 로고
    • Primal-dual interior point methods for self-scaled cones
    • Y. E. NESTEROV AND M. TODD, Primal-Dual Interior Point Methods for Self-Scaled Cones, SIAM J. Optim., 8 (1998), p. 324-364.
    • (1998) SIAM J. Optim. , vol.8 , pp. 324-364
    • Nesterov, Y.E.1    Todd, M.2
  • 27
    • 0002821681 scopus 로고
    • A recipe for semidefinite relaxation for 0-1 quadratic programming
    • S. POLIJAK, 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
    • Polijak, S.1    Rendl, F.2    Wolkowicz, H.3
  • 28
    • 0010504752 scopus 로고    scopus 로고
    • Computational advances using the reformulation-linearization technique (rlt) to solve discrete and continuous nonconvex problems
    • H. D. SHERALI AND W. P. ADAMS, Computational advances using the reformulation-linearization technique (rlt) to solve discrete and continuous nonconvex problems, Optima, 49 (1996), pp. 1-6.
    • (1996) Optima , vol.49 , pp. 1-6
    • Sherali, H.D.1    Adams, W.P.2
  • 29
    • 0023454146 scopus 로고
    • Quadratic optimization problems
    • N. Z. SHOR, Quadratic optimization problems, Soviet J. Comput. Systems Sci., 25 (1987), pp. 1-11; originally published in Tekhnicheskaya Kibernetika, 1 (1987), pp. 128-139.
    • (1987) Soviet J. Comput. Systems Sci. , vol.25 , pp. 1-11
    • Shor, N.Z.1
  • 30
    • 0023454146 scopus 로고
    • N. Z. SHOR, Quadratic optimization problems, Soviet J. Comput. Systems Sci., 25 (1987), pp. 1-11; originally published in Tekhnicheskaya Kibernetika, 1 (1987), pp. 128-139.
    • (1987) Tekhnicheskaya Kibernetika , vol.1 , pp. 128-139
  • 32
    • 0030106462 scopus 로고    scopus 로고
    • Semidefinite programming
    • L. VANDENBERGHE AND S. BOYD, Semidefinite programming, SIAM Rev., 38 (1996), pp. 49-95.
    • (1996) SIAM Rev. , vol.38 , pp. 49-95
    • Vandenberghe, L.1    Boyd, S.2
  • 33
    • 84923745334 scopus 로고    scopus 로고
    • Semidefinite programming for the graph partitioning problem
    • to appear
    • H. WOLKOWICZ AND Q. ZHAO, Semidefinite programming for the graph partitioning problem, Discrete Applied Math., to appear.
    • Discrete Applied Math.
    • Wolkowicz, H.1    Zhao, Q.2
  • 34
    • 0000549997 scopus 로고    scopus 로고
    • Approximating quadratic programming with bound and quadratic constraints
    • Y. YE, Approximating Quadratic Programming with Bound and Quadratic Constraints, Math. Programming, 84 (1999), pp. 219-226.
    • (1999) Math. Programming , vol.84 , pp. 219-226
    • Ye, Y.1
  • 35
    • 0004212716 scopus 로고    scopus 로고
    • Interior point algorithms: Theory and analysis
    • John Wiley, New York
    • Y. YE, Interior Point Algorithms: Theory and Analysis, Wiley-Intersci. Ser. Discrete Math. Optim., John Wiley, New York, 1997.
    • (1997) Wiley-intersci. Ser. Discrete Math. Optim.
    • Ye, Y.1
  • 37
    • 0003072982 scopus 로고    scopus 로고
    • Semidefinite programming relaxations for the quadratic assignment problems
    • Q. ZHAO, S. E. KARISCH, F. RENDL, AND H. WOLKOWICZ, Semidefinite programming relaxations for the quadratic assignment problems, J. Combin. Optim., 2 (1998), pp. 71-109.
    • (1998) J. Combin. Optim. , vol.2 , pp. 71-109
    • Zhao, Q.1    Karisch, S.E.2    Rendl, F.3    Wolkowicz, H.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.